Carol put some green and red unit cubes in a box. The ratio of the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5. A) how many green cubes are there in the box B) how many red cubes does carol have in the end

Answer: his speed when skateboarding is 6 mph and when walking is 3 mph

Step-by-step explanation:

Let x represent Marlon's walking speed.

Marlins speed on his skateboard is 2 times his walking speed. This means that his skating speed would be 2x.

At 1:30 Marlon left his house to go to the beach a distance of 6.75 mi. He rode his skateboard until 2:15. This means that the total time he spent skating is 45 minutes = 45/60 = 0.75 hours

Distance = speed × time

Distance covered while skating would be

2x × 0.75 = 1.5x

He walked the rest of the way. He arrived at the beach at 3:00. This means that the time that he spent walking is 45 minutes = 0.75 hours.

Distance covered while walking would be

x × 0.75 = 0.75x

Total distance covered is 6.75 miles. Therefore

1.5x + 0.75x = 6.75

2.25x = 6.75

x = 6.75/2.25

x = 3 miles per hour

His skating speed = 2 × 3 = 6 miles per hour.

Answer:

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

Step-by-step explanation:

Given:

Let

A(x₁ , y₁) = (1 , 4) and  

B( x₂ , y₂ ) = (-1 , 2)

To Find:

θ = ?

Solution:

Slope of a line when two points are given is given bt

[tex]Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Substituting the values we get

[tex]Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1[/tex]

Also Slope of line when angle ' θ  ' is given as

[tex]Slope=\tan \theta[/tex]

Substituting Slope = 1 we get

[tex]1=\tan \theta[/tex]

[tex]\tan \theta=1\\\theta=\tan^{-1}(1)[/tex]

We Know That for angle 45°,

tan 45 = 1

Therefore

[tex]\theta=45\°[/tex]

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

The slope of the budget line for a consumer who has $100 to spend per day, with product A at $7/unit on the horizontal axis and product B at $15/unit on the vertical axis, is -0.47. More consumption of one good requires a sacrifice in the consumption of the other.

The subject of this question is the slope of the budget line in microeconomics, which represents the trade-off between two goods, product A and product B. It can be determined by dividing the price of the good on the horizontal axis (product A) by the price of the good on the vertical axis (product B). Hence, the slope of the budget line is $7/$15 = 0.47 (rounded to two decimal places). The slope is negative reflecting the fact that to obtain more of one good, a consumer needs to give up some of the other.

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The slope of the budget line is -7/15 or approximately -0.467.

       In this case, the slope = - (7 / 15).

After calculating, we get the slope as - 7/15 or approximately -0.467. This slope indicates the rate at which the consumer can trade product A for product B while staying within their budget.

Answer:

The option [tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex] is correct

The difference of the given expression is

[tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})=\frac{(x+5)(x+2)}{x^3-9x}[/tex]

Step-by-step explanation:

Given expression is [tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})[/tex]

To find the difference of the given expression as below :

[tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})[/tex]

[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x^2-9)})-({\frac{x+1}{x^2-9})[/tex]

[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x^2-3^2)})-({\frac{x+1}{x^2-3^2})[/tex]

[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x-3)(x+3)})-({\frac{x+1}{(x-3)(x+3)})[/tex]  

( using the formula [tex]a^2-b^2=(a+b)(a-b)[/tex] )

[tex]=\frac{2x+5(x+3)-(3x+5)-x(x+1)}{x(x-3)(x+3)}[/tex]

[tex]=\frac{2x^2+6x+5x+15-3x-5-x^2-x}{x(x-3)(x+3)}[/tex] (adding the like terms)

[tex]=\frac{x^2+7x+10}{x(x^2-9)}[/tex] ( by factoring the quadratic polynomial )

[tex]=\frac{(x+5)(x+2)}{x^3-9x}[/tex]

Therefore [tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})=\frac{(x+5)(x+2)}{x^3-9x}[/tex]

Therefore the difference of the given expression is

[tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex]

Therefore option [tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex] is correct

Answer:

A

Step-by-step explanation:

Answer:

(-138) is the answer.

Step-by-step explanation:

Perfect square numbers between 15 and 25 inclusive are 16 and 25.

Sum of perfect square numbers 16 and 25 = 16 + 25 = 41

Sum of the remaining numbers between 15 and 25 inclusive means sum of the numbers from 17 to 24 plus 15.

Since sum of an arithmetic progression is defined by the expression

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

Where n = number of terms

a = first term of the sequence

d = common difference

[tex]S_{8}=\frac{8}{2} [2\times 17+(8-1)\times 1][/tex]

   = 4(34 + 7)

   = 164

Sum of 15 + [tex]S_{8}[/tex] = 15 + 164 = 179

Now the difference between 41 and sum of perfect squares between 15 and 25 inclusive = [tex]41-179[/tex]

= -138

Therefore, answer is (-138).

The sum of the perfect squares (16 and 25) between 15 and 25 is 41. The sum of all the other numbers between 15 and 25 is 179. So, when we subtract 179 from 41, we get -138.

To find the answer, we first need to identify which numbers between 15 and 25, inclusive, are perfect squares. A perfect square is a number which can be expressed as the product of an integer with itself. In this range, 16 and 25 are the perfect squares.

The sum of these perfect squares is 16 + 25 = 41.

Next, we need to find the sum of all the other numbers between 15 and 25, inclusive, that are not perfect squares. These numbers are 15, 17, 18, 19, 20, 21, 22, 23, and 24. Adding these numbers together gives a sum of 179.

Now subtract this second sum from the first to get the answer: 41 - 179 = -138

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Answer:

Itself is a Reflexive Pronoun.

Step-by-step explanation:

The reflexive pronouns are words that end with prefixes "self or selves".When the object and the subject in the sentence are same then reflexive pronoun is  used. That is  It is to denote that the subject is doing something by or to itself .These reflexive pronoun can act either as a direct object or indirect object . It is preceded by the adverb, adjective, pronoun, or noun  to which it refers to. They  also allow us to point back to, or reflect on, the subject of the sentence with clarity. The nine English reflexive pronouns are

Answer:

x = 1.64 in   the size of the side of the square

Step-by-step explanation:

Let call x side of the square to be cut from cornes, then:

First side of rectangular base

L = 14 - 2*x

And the other side

d = 8 -2*x

Then Volume of the box

V(b) = L*d*x

V(x) =  ( 14- 2*x ) * ( 8 -2*x)*x

V(x) = ( 112 -  28*x  -16*x + 4*x² )*x    ⇒  4*x³ - 44*x² + 112*x

Taking derivatives on both sides of the equation we get:

V´(x) = 12*x² - 88*x +112

V´(x) = 0       ⇒     12*x² - 88*x +112 = 0

A second degree equation, solvin it

3x² - 22*x +  28 = 0

x₁,₂ = [ 22 ± √484 - 336   ] / 6

x₁   =  (22 + 12,17) /6         x₂  =  ( 22 - 12.17 ) / 6

x₁   =  5.69     We dismiss this solution since it make side 8 - 2x  a negative length

 x₂  =  9.83/6      

x₂  =  1.64

Then x = x₂  = 1.64 in

Answer:

1.64 in

Step-by-step explanation:

a. The population for the study is a total of 1000 adults, so the 50% that favored the plan made up a total of 500 people, since 500 is 1/2 (or 50%) of 1000.

b. The percentage provided is an inferential statistic. Inferential statistics are made by taking a sample of a population and using that sample as data used to make inferences/predictions. Since the percentage provided is a sample of a population being used to make a prediction, it is an inferential statistic.

The population is all adults in the nation, and the sample is the 1000 adults surveyed. The provided percentage is a descriptive statistic, as it summarizes data from the sample.

In the context of this problem, the population refers to all adults across the nation, while the sample refers to the 1000 adults who were surveyed.

The percentage mentioned in the survey (50% in favor of breaking up the 12 megabanks) is a descriptive statistic. A descriptive statistic summarizes and represents data from a sample, which in this case is the surveyed group of 1000 adults. It does not aim to infer or predict facts about the larger population.

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The values of m and n are [tex]m=4[/tex] and [tex]n=1[/tex]

Explanation:

The two equations are [tex]m+n=5[/tex] and [tex]m-n=3[/tex]

From the equation [tex]m-n=3[/tex], we shall find the value of m such that

[tex]m=n+3[/tex]

Substituting the value of m in [tex]m+n=5[/tex], we get,

[tex]\begin{array}{r}{n+3+n=5} \\{2 n+3=5}\end{array}[/tex]

Subtracting both sides by 3,

[tex]2n=2[/tex]

Dividing both sides by 2, we get,

[tex]n=1[/tex]

Substituting [tex]n=1[/tex] in [tex]m-n=3[/tex]

[tex]\begin{array}{r}{m-1=3} \\{m=4}\end{array}[/tex]

Thus, the values of m and n are [tex]m=4[/tex] and [tex]n=1[/tex]

Answer:

no it is 8 more so do it  one more time and you will get the answer 352? fine the number

Step-by-step explanation:

Answer:

5.98 s

Step-by-step explanation:

576 ft = 576 / 3.28 = 175.56 m

Let g = 9.81 m/s2. The time it takes for the ball to fall from 165.56 m high to the ground is

[tex]s = gt^2/2[/tex]

[tex]t^2 = 2s/g = 2*175.56/9.81 = 35.8[/tex]

[tex]t = \sqrt{35.8} = 5.98 s[/tex]

Answer:

The average revenue per passenger = E(x) = $15.70

[tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{398} \approx 19.95[/tex]

b)$1,884 ± $20

Step-by-step explanation:

a)

Refer  attached fig for probability model,

i)The average revenue per passenger = E(x) = $15.70

[tex]\sigma^{2} = V[X] \sum _{x} (x-\mu )^{2} \times P(X=x)[/tex]

[tex]\sigma^{2} = (0-15.7)^{2} \times 0.54+(25-15.7)^{2} \times 0.34 +(60-15.7)^{2} \times 0.12[/tex]

[tex]\sigma^{2} = 133.1 + 29.4 + 235.5 = 398[/tex]

Standard Deviation = [tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{398} \approx 19.95[/tex]

ii)  average revenue per passenger = E(x) = $15.70

b) Revenue should the airline expect for a flight of 120 passengers

revenue = 120 * $15.70 = $1,884 ± $20 (or 19.95 rounded up)

use same σ

The average revenue per passenger is $15.2 and the standard deviation is $18.45. For a flight of 120 passengers, the airline may expect around $1824 with standard deviation of $202.33. We're assuming that each passenger's baggage habits are independent.

To solve this, first we'll construct a probability model. Let X be a random variable denoting the revenue from each passenger. Then X can take three possible outcomes: $0 (with probability 0.54), $25 (with probability 0.34) or $60 (with probability 0.12).

The average revenue from each passenger E(X), also known as the expected value of X, is calculated as follows:

E(X) = 0*0.54 + 25*0.34 + 60*0.12 = $15.2

The standard deviation of X, denoted σ(X), is computed as follows:

σ(X) = sqrt[(0-15.2)^2*0.54 + (25-15.2)^2*0.34  + (60-15.2)^2*.12] = $18.45

Given this, for a flight of 120 people, the total expected revenue is 120*$15.2 = $1824 and the standard deviation of total revenue would be sqrt(120)*$18.45 = $202.33.

The underlying assumption here is that the baggage habits of passengers are independent, which is reasonable in this case.

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Answer:

The equation representing the problem is [tex]x=\frac{24\times 6}{32}[/tex].

Mr. Patel used 5 bags of seeds.

Step-by-step explanation:

Given:

Number of times bird feeder refilled =24

Number of cups of seeds used each time = 6 cups

Number of seeds each bag holds = 32 cups.

We need to write the equation to represent the problem.

Solution.

Let the total number of bag of seed be 'x'.

First we will find the Total number of cups of seeds used.

Now we can say that;

Total number of cups of seeds used can be calculated by multiplying Number of times bird feeder refilled by Number of cups of seeds used each time.

framing in equation form we get;

Total number of cups of seeds used = [tex]24\times6 \ cups[/tex]

Now We know that;

1 bag holds = 32 cups

Total number of bags required = [tex]24\times6 \ cups[/tex]

So we can say that;

Total number of bags required is equal to Total number of cups of seeds used divided by number of seed hold by each bag.

framing in equation form we get;

[tex]x=\frac{24\times 6}{32}[/tex]

Hence the equation representing the problem is [tex]x=\frac{24\times 6}{32}[/tex].

On solving we get;

[tex]x=4.5[/tex]

Since bags cannot be bought in half or in decimal value.

Hence we can say Mr. Patel used 5 bags of seeds.

Answer:

  y = 2sin((π/7)x)

Step-by-step explanation:

The graph goes through (0, 0) and has a range of ±2. This matches a sine function with an amplitude (A) of 2 and a vertical offset (C) of zero.

The half-period is 7, so the value of k is such that 7k = π, or k = π/7.

The desired function is y = 2·sin((π/7)x).

Final answer:

The statement is true; the centroid of a triangle is the point that lies 2/3 of the way from each vertex to the midpoint of the opposite side. The centroid is the same point for all three vertices, which can be shown using vector operations that equate to (A+B+C)/3 for a triangle with vertices A, B, and C.

Explanation:

The statement that points lying 2/3 of the way from a vertex to the midpoint of the opposite side for any triangle in ℝ² (the real number plane) are all the same point, and this point is called the centroid of the triangle, is True. To prove this, consider a triangle ABC with vertices A, B, and C. If M is the midpoint of side BC, N is the midpoint of side AC, and O is the midpoint of side AB, then the points two-thirds of the way from the vertices A, B, and C to the midpoints of the opposite sides, respectively, can be represented by the vectors (2M+A)/3, (2N+B)/3, and (2O+C)/3.

Applying the midpoint formula and vector addition, we find that these points are equivalent to (B+C)/3, (A+C)/3, and (A+B)/3 respectively, which, when simplified, all yield to (A+B+C)/3, illustrating that the points coincide and thus prove the existence of a single centroid.

In a geometric context, the centroid is the point where the triangle’s medians intersect, and it also serves as the triangle's center of mass. The centroid divides each median in a 2:1 ratio, with the larger portion being closer to the vertex. This property is intrinsic to triangles and can be demonstrated using vector algebra or geometric arguments.

Answer: 55 performances are needed to break even.

Step-by-step explanation:

Let x represent the number of musical performances that are made.

Producing a musical costs $88,000 plus $5900 per performance. This means that the total cost of x musical performances would be

88000 + 5900x

One sold-out performance earns $7500 in revenue. If every performance sells out, it means that the total revenue would be

7500 × x = 7500x

In order to break even, total cost would be equal to total revenue. Therefore,

7500x = 88000 + 5900x

7500x - 5900x = 88000

1600x = 88000

x = 88000/1600 = 55

The type of annuity in the question is known as a refunded annuity. It ensures that the entire contract value is utilized in case the annuitant dies prematurely. The payments would continue to a beneficiary until the total contract value has been paid.

The type of annuity described in the question, where payments continue to a beneficiary until the contract value is paid out if the annuitant dies prematurely, is referred to as a refunded annuity. Annuities are often used in retirement planning. This specific type of annuity gives protection to the annuitant's investment, ensuring that the whole amount of the contract value is utilized even if the annuitant dies before receiving the full value in payments. For instance, if an annuitant bought an annuity worth $200,000 and dies after receiving only $50,000, the beneficiary would continue to receive payments until the remaining $150,000 is paid out.

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A cash refund annuity is an annuity that promises to continue payments to a beneficiary until the contract value has been paid if the annuitant dies before that.

The type of annuity described in the question, where the payments continue to a beneficiary until an amount equal to the contract value has been paid if the annuitant dies before that, is called a cash refund annuity.

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Answer:sas

Step-by-step explanation:

Answer:

IS THE ANSWER

Answer:

Perimeter= 12 feet   Area= 6 feet (squared)

Step-by-step explanation:

Perimeter= Adding all the sides together, that means it is 3+4+5= 12 feet

Area= Hight times base divided by 2. Because hight times base is area of a rectangle, and a right triangle (and all other triangles) is half of it. Because it is a right triangle, its hight must be 3 or 4, and base also 3 or 4. But no the same number twice, so 3*4=12, 12/2=6 feet (squared).

I hope that helped! =)

Answer:Lilah's speed on the train is 60 mph and Mason's speed is 75 mph

Step-by-step explanation:

Let x represent the speed of Lilah.

Lilah is moving from Portland to Seattle. It takes her 3 hours to go by train.

Distance = speed × time

Distance covered by Lilah in moving from Portland to Seattle would be

3 × x = 3x

It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train.

It means that Mason's speed is

x + 15

Distance covered by Mason would be

2.4(x + 15) = 2.4x + 36

Since the distance from Portland to Seattle is the same, then

3x = 2.4x + 36

3x - 2.4x = 36

0.6x = 36 x = 36/0.6 = 60 mph

Mason's speed would be 60 + 15 = 75 mph

Answer:

B on edu2020

Step-by-step explanation:

To find the point of intersection between the given exponential function and the horizontal line, substitute the y-value (115) into the equation and solve for x.

To find the point of intersection between the exponential function y=(1-25)^x-2/5 and the horizontal line y=115, we can substitute the given y-value (115) into the equation and solve for x. By substituting y=115 into y=(1-25)^x-2/5, we can rewrite the equation as 115=(1-25)^x-2/5. This allows us to solve for x and find the x-coordinate of the point of intersection.

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To find the intersection point, substitute the y-coordinate (115) into the exponential function and solve for x using ln(1-25).

To find the intersection point between the exponential function and the horizontal line, we substitute the y-coordinate of the intersection point (which is 115) into the given exponential function. We then solve for x.

Substituting y = 115 into the exponential function, we have (1-25)^(x-2/5) = 115. Taking the natural logarithm of both sides, we get (x-2/5)ln(1-25) = ln(115). Solving for x, we divide both sides by ln(1-25) and add 2/5 to get x = ln(115)/ln(1-25) + 2/5.

Therefore, the intersection point is (x, 115), where x = ln(115)/ln(1-25) + 2/5.

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The insurance costs £602.02 now.

Step-by-step explanation:

Amount paid for car insurance = £635.71

Price reduce = 5.3%

Amount of reduce = 5.3% of amount paid

Amount of reduce = [tex]\frac{5.3}{100}*635.71[/tex]

Amount of reduce = [tex]0.053*635.71[/tex]

Amount of reduce =  £33.69263

Rounding off to two decimal place

Amount of reduce =  £33.69

Reduced price = Amount paid - Amount of reduce

Reduced price = 635.71 - 33.69 =  £602.02

The insurance costs £602.02 now.

Keywords: subtraction, division

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Original price × (1 - reduction percentage) = Reduced price. £635.71 × (1 - 0.053) ≈ £602.97 (rounded to 2 DP).

let's break it down step by step:

1. Calculate the reduction amount:

  Multiply the original price (£635.71) by the reduction percentage (5.3% or 0.053).

  Reduction Amount = £635.71 * 0.053

2. Subtract the reduction amount from the original price:

  Subtract the reduction amount from the original price to find the reduced price.

  Reduced Price = £635.71 - Reduction Amount

Now, let's plug in the values:

1. Calculate the reduction amount:

  Reduction Amount = £635.71 * 0.053

                   ≈ £33.73763

2. Subtract the reduction amount from the original price:

  Reduced Price = £635.71 - £33.73763

                ≈ £602.97237

Rounded to two decimal places:

Reduced Price ≈ £602.97

So, after the 5.3% reduction, Terry's car insurance costs approximately £602.97.

Answer:

The answer to your question is below

Step-by-step explanation:

Functions

  f(x) = 12x           f⁻¹(x) = 2x

a)   f⁻¹(-2) = 2(-2)

     f⁻¹(-2) = -4

b) f(-4) = 12x

    f(-4) = 12(-4)

    f(-4) = -48

c) f(f⁻¹(-2)) =

   f(f⁻¹(x)) = 12(2x) = 24x

  f(f⁻¹(-2)) = 24(-2) = -48            

I think your functions are wrong they must be       f(x) = 1/2x    f⁻¹(x) = 2x        

a)  f⁻¹(-2) = 2(-2)

             = -4

b) f(-4) = 1/2(-4)

         = -2

c) f(f⁻¹(x)) = 1/2(2x)

              = x

  f(f⁻¹(-2)) = -2

Answer:

1)= -4

2)= -2

3)= -2

Step-by-step explanation:

Answer:

4 minutes - |12 x 4 = 48|    |48 + 14 = 62|    Charles = 62

10 x 4 = 40|     40 + 22 = 62

Step-by-step explanation:

If he has 14 all we have to do is keep multiplying 12 by x and 10 by x add them to their correct person until Charles has more eggs broken then Louis

Answer:

The answer to your question is vo = 19.62 m/s

Step-by-step explanation:

Data

angle = α = 30°

time = t = 2 s

vo = ?

g = 9.81 m/s²

Formula

                  [tex]t = \frac{2vosin\alpha}{g}[/tex]

Solve for vo

             [tex]vo = \frac{tg}{2sin\alpha}[/tex]

Substitution

            [tex]vo = \frac{(2)((9.81)}{2sin 30}[/tex]

Simplification

           [tex]vo = \frac{19.62}{2(0.5)}[/tex]

           [tex]vo = \frac{19.62}{1}[/tex]

Result

            vo = 19.62 m/s

Answer:

A

Step-by-step explanation

You need to subtract the 3 1/5 from both sides, which gives you 29/5

Answer:

A

Step-by-step explanation:

You always to the opposite of the opporation already given.

Answer:

1. Ernest has $82.5 and Gene has $117.5

2. c) 125x + 1500 = $20000

Step-by-step explanation:

If we mark Gene's half dollars with x, then it is given that Ernest has 8 more, which is x+8.

It is also given that Ernest has no quarters, but Gene has them as many as Ernest has half dollars, which is x+8.

And it is given that they both have 45 dimes each, which is $4.5 each.

Now, let's add up all these numbers:

Ernest: (x+8)•0.5 + 0•0.25 + 4.5 = 0.5x + 8.5

Gene: x•0.5 + (x+8)•0.25 + 4.5 = 0.75x + 6.5

They collected $200 together which means:

0.5x + 8.5 + 0.75x + 6.5 = $200

1.25x + 15 = $200

If we want to avoid decimal number, we can multiply whole equation with 100:

125x + 1500 = $20000

so, the correct answer is C.

Finally, to find x:

125x = 18500

x = 148

Ernest had 0.5x + 8.5 which is $82.5

Gene had 0.75x + 6.5 which is $117.5

Answer:

a) [tex] P(t) =1600 +50t[/tex]

b) [tex] P(t) = 1600 (1.05)^t[/tex]

Step-by-step explanation:

Assuming the complete question : "A town has a population of 1000 people at time t = 0. In each of the following cases, write a formula for the population, P, of the town as a function of year t. (a) The population increases by 50 people a year. (b) The population increases by 5% a year."

Part a

For this case we can use a linear model in order to estimate the population size since we have a fixed increase each year. So our model would be given by:

[tex] P(t) = P_o + b t[/tex]

Where [tex] b =50[/tex] on this case since represent the increase per year of the slope for the linear model. And the initial amount is [tex] P_o = 1600[/tex], so then the model is:

[tex] P(t) =1600 +50t[/tex]

Part b

For this case we have a rate of increase and when we have this the lineal model is not the most appropiate. So then we can use an exponential model given by:

[tex] P(t) =P_o b^{t}[/tex]

Where [tex] P_o = 1600[/tex] represent the initial population and for this case b is the rate of increase [tex] b = 1+0.05 = 1.05[/tex] since each year we have an increase of 5% and t is the time. So then the model is given by:

[tex] P(t) = 1600 (1.05)^t[/tex]

The population of a town can be calculated through formulas for linear growth (P = P0 + rt) and exponential growth (P = P0 * e^(rt)), depending on whether the population grows by a fixed amount or percentage each year. To use these formulas, the specific growth rate of the town is needed.

The subject of the question is about writing formulas for population growth. Let's denote the initial population as P0, the rate of growth as r and the time in years as t. Here are two common formulas:

To use these formulas, you'd need to know the specific growth rate of the town. It's also important to remember that actual population changes can be more complex and may not follow these exact formulas.

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