Is my answer correct?
Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).

Answers

Answer 1

Here is the answer to the given problem above.
Here is the exponential function to model this situation:
f(x) = 420(0.79)x
Now, solve with the given values.
P(t)=420×(.79)^t P(5)=420×(.79)^5=129
So the answer would be 129 animals.
Hope this answer helps. Thanks for posting your question!

Answer 2

Answer:

[tex]y=420\cdot (0.79)^x[/tex]

The value of the function after 5 years would be 129.

Step-by-step explanation:

We have been that a population of 420 animals decreases at an annual rate of 21%. We are asked to write an exponential function for our given problem.

We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value,

b = For decay b is in form [tex]1-r[/tex], where, r represents decay rate in decimal form.

[tex]r=21\%=\frac{21}{100}=0.21[/tex]

[tex]y=a\cdot (1-r)^x[/tex]

[tex]y=420\cdot (1-0.21)^x[/tex]

[tex]y=420\cdot (0.79)^x[/tex]

Therefore, our required function would be [tex]y=420\cdot (0.79)^x[/tex].

To find the value of the function after 5 years, we will substitute [tex]x=5[/tex] in our function.

[tex]y=420\cdot (0.79)^5[/tex]

[tex]y=420\cdot 0.3077056399[/tex]

[tex]y=129.236368758[/tex]

[tex]y\approx 129[/tex]

Therefore, the value of the function after 5 years would be 129.

Related Questions

How do i describe the shape of the graph of each cubic function by determining the end behavior and number of turning points?
for ex. y=3x^3-x-3 ...?

Answers

A cubic is conventionally pictured as a rising curve, passing through a maximum and then a minimum before rising again - a double-humped curve. But depending on the relative sizes of the coefficients of the terms, and hence the proportion of functions with even or odd symmetry, the overall shape may differ widely. In particular, if the terms with odd symmetry dominate, the curve may not show either a maximum or a minimum, with the slope always of the same sign ie it is monotonically increasing or decreasing.

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Which of the following is the inverse function of y = 3x + 1?

x = 3y + 1
y = (1/3)x + 1/3
y = (x – 1)/3
y = x/3 - 1

Answers

y= (x-1) /3 is the correct answer

Answer:

Option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]

Step-by-step explanation:

[tex]y=3x+1[/tex]

For finding the inverse of this function, we will interchange x and y, then solve for y.

[tex]3y=x-1[/tex]

[tex]y=\frac{x-1}{3}[/tex]

Hence, option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]

The figure below shows circle with center O and regular hexagon ABCDEF constructed inscribed in a circle.Which of the following steps will help prove that triangle FBD is equilateral?

Answers

Final answer:

Triangle FBD in the given regular hexagon inscribed in a circle can be proven to be an equilateral triangle based on the equal lengths of radii and the angle of 60 degrees subtended at the center by the side of the hexagon.

Explanation:

To prove that triangle FBD is an equilateral triangle, we first need to understand a few properties of a regular hexagon and a circle. In a regular hexagon inscribed in a circle, every angle at the center of the circle subtended by the sides of the hexagon is 60 degrees because the total degree measure at the center of the circle is 360, and this is divided equally among the six sides of the hexagon.

Triangle FBD is formed by joining the center of the circle, O, and two consecutive vertices of the hexagon, B and F. As the hexagon is regular and inscribed in a circle, both OB and OF are radii of the circle. By definition, all radii of a given circle are equal in length. Therefore, OB = OF.

The angle BFO subtended at the center by the side BF of the hexagon is 60 degrees. Hence, triangle FBD is an equilateral triangle because it has two equal sides and the included angle is 60 degrees, which are the properties of an equilateral triangle.

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Final Answer:

To prove that triangle FBD is equilateral, one can show that the central angles corresponding to the three sides of the hexagon (angle AOB, angle BOC, and so on) are all equal. Therefore, demonstrating that angle FOB, angle BOD, and angle DOF are each 120 degrees will establish that triangle FBD is equilateral.

Explanation:

In a regular hexagon inscribed in a circle, the central angles formed by connecting the center of the circle (O) to consecutive vertices of the hexagon are all equal. Since each interior angle of a regular hexagon is 120 degrees, the central angles (e.g., angle AOB, angle BOC, etc.) are also 120 degrees. To prove that triangle FBD is equilateral, one needs to focus on the central angles corresponding to its sides.

The central angles associated with triangle FBD are angle FOB, angle BOD, and angle DOF. By demonstrating that each of these angles is 120 degrees, it can be concluded that triangle FBD is equilateral. The regularity of the hexagon ensures that the central angles are equal, making this an effective and straightforward way to prove the equilaterality of triangle FBD.

In conclusion, to establish the equilaterality of triangle FBD, one should emphasize the properties of central angles within the context of a regular hexagon. Specifically, showing that angle FOB, angle BOD, and angle DOF are each 120 degrees serves as a valid proof for the equilateral nature of triangle FBD within the given geometric configuration.

A plumber charges a $45 fee to make a house call and then $25 for each hour of labor. The plumber uses an equation in the form y=mx +b to determine the amount to charge each customer. What is the value of m in the equation?

Answers

m=slope
In this case the slope would be $25
y=mx+b
y=25x+45

Answer: m=25

Answer:

Let x represents the number of hours of labor and y represents the total charges.

Since, in the given situation,

The total charges = A fixed charge for house call + Extra charge per hours,

Fixed charge for house call = $ 45,

Extra charges for every hour = $ 25,

⇒ Extra charge for x hours = 25 x,

Thus, the total charges for x hours,

y = 45 + 25 x

Which is the required equation that will use to determine the amount to charge each customer.

By comparing this equation with y = mx + c,

m = 25

is (4,2) a solution to the system y-x=2 and -3x -2y= -8

Answers

to figure out the answer here, all you have to do is plug the given point into your equations and see if the result is true:

(4, 2) .... aka (x, y)

2 - 4 = 2
-2 = 2 ... this one is FALSE, as -2 doesn't equal 2, so already you can tell that the point won't be a solution, but still, check the second equation.

-3(4) - 2(2) = -8
-12 - 4 = -8
-16 = -8 .... this one is also false. (4, 2) is not a solution for this system of equations.

what is the greatest common factor of 51 and 68

Answers

the greatest common factor of 51 and 68 would be the largest positive integer that divides both of those numbers without a reminder. so that would be the GCF of 51&68.

what is 40% in fraction form

Answers

Since we have 40 out of 100
40/100 reduces to 4/10
but then dividing 4 by 2 and 10 by 2 we have 2/5

To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. In this case, 40% can be written as the ratio 40 to 100 or [tex]\frac{40}{100}[/tex]. Notice however that [tex]\frac{40}{100}[/tex] is not in lowest terms so we need to divide the numerator and the denominator by 20 which gives us [tex]\frac{2}{5}[/tex].

195 s; minutes
a. 4.5 min
b. 3 min
c. 3.25 min
d. 2.5 min

Answers

c)3.25
195÷60=3.25
every min is 60 seconds

it would be C.3.25 mins

hope this helps you

What does 15/6 equal turned into a mixed fraction?

Answers

Your answer is 2 1/2. :)

15/6....how many times does 6 go into 15 without going over ? It goes in there 2 times. 2 x 6 = 12. So 2 is ur whole number. Now take 15 and subtract 12 which gives u 3...that is ur numerator...the denominator stays the same.
so ur mixed number is 2 3/6...but ur 3/6 reduces making ur mixed number be
2 1/2

PLEASE HELP ME IM TRYING TO GET THIS DONE AND NOBODY IS HELPING ME Triangle ABC below is reflected over the y-axis.
a What are the coordinates of the reflected triangle
b Describe in words what happened to the x coordinates and the y coordinates of the original triangles vertices as a result of this reflection

Answers

y axis reflected, just imagine it
means all x values are going to turn negative
initial values:
A=(1,3)
B=(4,5)
C=(3,1)

reflected
A'=(-1,3)
B'=(-4,5)
C'=(-3,1)

A.
the reflected coordinates are A'=(-1,3), B'=(-4,5), C'=(-3,1)

B. the x coordinates flip flopped, they turned negative, y coordinates stayed the same

A winter jacket is marked down 75% from its original price. according to the new price tag, it now costs $52.50. what was the original price? $210.00

Answers

Yes you are right there

Which is the graph of linear inequality x-2y>-12 help!

Answers

Answer:

The below attached graph shows the given inequality.

Step-by-step explanation:

Here, the given inequality,

x - 2y > -12

Since, related equation of the inequality,

x - 2y = -12

Which is a line passes through (-12, 0) and (0, 6)

Also, '>' represents dotted line,

So, join these two points by dotted line in the coordinate plan,

Now,

0 - 2(0) > -12 (True)

i.e. shade the region of the line that contains origin.

By the above explanation we will get the graph of given inequality ( shown below )

Reg sells cars. he makes a base salary of $25,000, plus $1500 per car he sells. the function that models this situation is s = 1500x 25000. after working at the car dealership for 2 years, he gets a raise. he now makes $1700 per car he sells. what is the new function that models this situation?

Answers

s1=1700x+25000. s1 for new function or any letter you prefer to represent y

Create a log expression, using the laws of logs, that simplifies to 7^x = 64.

This makes no sense to me! Help!

What are the log laws?

Answers

x = log65 (base 7 logs)

Final answer:

To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.

Explanation:

To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.

First, we can rewrite the exponential equation as a logarithmic equation, which is x = log7(64).Next, we can use the logarithmic property that states logb(ax) = x * logb(a). Applying this property, we have x = log7(26) = 6 * log7(2).

Therefore, the log expression that simplifies to 7^x = 64 is x = 6 * log7(2).

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Marta walked at 3.9 miles per hour for 0.72 hours. How far did she walk?

Answers

3.9 x 0.72 = 2.808????????

this is a porportion, she is walking 3.9 every hour so that is 3.9/1 (1 representing the one hour) and she only walked .72 hours and we dont know far she walked for, so its x/.72 we cross multiply (not cross cancel) and we get 3.9×.72=x
we multiply those decimals and we get 2.808 miles she had walked. Hope that helps.

Which term describes the dotted line in the quadrilateral?
A. vertex
B. side
C. diagonal
D. angle ...?

Answers

The best and most correct answer among the choices provided by your question is the third choice or letter C.

A diagonal is the term that describes the dotted line in the quadrilateral.

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On average, sloths spend 16.5 hours per day sleeping. what percent of the day do sloths spend sleeping? round your answer to the nearest percent.

Answers

Unknown if you wanted to be clever
on average means typically so there is data called "outliers"
Moreover it doesn't say what average percent of the day and it doesn't mention the planet, namely Earth..
there could be sloths on other planets and those other planets are likely to have different hours in the day.

Three dentists wanted to compare the ages of their patients. They each calculated their patients’ mean age and the mean absolute deviation of their ages. They displayed the results in a table.
Which statements are true?
Choose exactly two answers that are correct.
DentistMean patient ageMAD
Appiah439.7
Cantwell2913.9
Singh4114.1
A. Dr. Appiah’s patients’ ages vary more than do Dr. Cantwell’s patients’ ages.
B. Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.
C. Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount.

Answers

B. Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.

C. Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount.

The product of 8 and the sum of 4 and a number is 112. What is the number?

Which equation could be used to solve for the number?

Answers

Product of 8 and the sum of 4 and a number:

sum of 4 and a number: (4 + n)

Product of 8

8 x (4 + n) is 112

8 x (4 + n) = 112

Distribute

32 + 8n = 112

Subtratc

8n = 80

Divide by 8

n = 10

The number is 10, and next time please put options because it says "Which equation could be used to solve for the number?"

You probably are supposed to use PEMDAS (the order of operations) to represent this equation so i would choose C.

It sounds like 8*(n+4)=112 then you have simple algebraic equation that could be solved by a TI-Calculator or by hand
Divide both sides by 8
Subtract four from both sides
You're left with n= the answer

What number is 0.77% of 900?

Answers

6.93

is what youre looking for

the ans is 693 becoz 0.77%=77/100*900=693

Baby jacobs birth weight was 10 pounds one week after being born his weight was 9 pounds what was the percent of decrease in jacobs weight

Answers

Baby Jacobs weight has decreased by 10% in just one week.

its 10%.

hope this helps you

The table shows the result of a restaurant survey.
Meals Service Good Service poor Total
Lunch 49 39 88
Dinner 19 15 34
Total 68 54 122
Find the probability the service was poor, given that the meal was dinner.

Answers

If the meal was dinner there were total of 34 that have been in the survey. Out of those 34, 15 of them said that service was poor.

That simply means that 15/34 is the probability that the service was poor if you are taking dinner.

PLEASE HELP AND BRAINLYEST ANSWER TO CORRECT ANSWER

Answers

The answer to your question is 2/19

Solve for x. Express the answer in simplest form.

Answers

6x-1 = 5*3
6x-1=15
6x=16
3x=8
x = 8/3
x= 2[tex] \frac{2}{3} [/tex]

Our starting equation looks like this:
[tex] \frac{6x-1}{5} = \frac{3}{1} [/tex]

First we multiply each side by 5 to get rid of fractions. we get:
6x - 1 = 3*5

now we switch -1 to oposite side of equal sign. It will also change its sign to +1
6x = 15 + 1
6x = 16

now we divide both sides with 6 and we get:
x = 16/6 = 8/3

answer is:
x = 8/3

The marginal revenue function on sales of q units of a product is R'(q)=240-18√q dollars per unit.

Estimate the total revenue if sales are 100 units.
What is the marginal revenue at 100 units?
Estimate the total revenue if sales are 101 units.
...?

Answers

Total revenue R(q) = ∫R'(q) dq = ∫(240 - 18√q)dq = 240q - 12q^3/2
R(100) = 240(100) - 12(100)^3/2 = 24000 - 12(1000) = $12,000

Marginal revenue at 100 units R'(100) = 240 - 18√100 = 240 - 18(10) = $60

Revenue at 101 units = R(101) = 240(101) - 12(101)^3/2 = 24,240 - 12,180 = $12,060

Final answer:

The marginal revenue for 100 units sold is 180 dollars per unit. We cannot precisely estimate the total revenue for 100 or 101 units sold without further information.

Explanation:

In this problem, we're dealing with the concept of marginal revenue. The marginal revenue function gives us the change in total revenue for each additional unit sold. That is given in this case as R'(q)=240-18√q.

To find the marginal revenue at 100 units, we simply substitute q = 100 into our function: R'(100)=240-18√100 = 240 - 18*10 = 180 dollars per unit.

The total revenue given a specific quantity is typically found by integrating the marginal revenue function. However, without the constants of integration or the original revenue function, we cannot accurately compute the total revenue for 100 or 101 units sold in this case.

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solve the equation. Check for extraneous solutions.

[tex]2|7-7x|=2x+4 [/tex]

Answers

2(7-7x) = 2x + 4
14 - 14x = 2x +4
16x = 10
x = 10/16
x = 0.625

2[-(7-7x)] = 2x + 4
-14 +14x = 2x + 4
12x = 18
x = 18/12
x = 1.5

answer:
solutions x = 0.625 and x = 1.5

Answer: The answer is [tex]\dfrac{5}{8},~\dfrac{3}{2}[/tex] and no extraneous solution.

Step-by-step explanation: The given equation is

[tex]2|7-7x|=2x+4.[/tex]

We are given to solve this equation and also find its extraneous solution.

The solution is as follows:

[tex]2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=\dfrac{5}{8},~~~~~~~~~~~~~~~~~\Rightarrow x=\dfrac{3}{2}.[/tex]

now, for [tex]x=\dfrac{5}{8}[/tex], we have

[tex]L.H.S.=2|7-7\times \dfrac{5}{8}|=\dfrac{21}{4},\\\\R.H.S.=2\times\dfrac{5}{8}+4=\dfrac{21}{4}.[/tex]

So, this solution is not extraneous.

For [tex]x=\dfrac{3}{2}[/tex], we have

[tex]L.H.S.=2|7-7\times \dfrac{3}{2}|=7,\\\\R.H.S.=2\times\dfrac{3}{2}+4=7.[/tex]

So, this solution is also not extraneous.

Hence, the solution is [tex]\dfrac{5}{8},~\dfrac{3}{2}[tex] and there is no extraneous solution.

An equation of the line tangent to y=sinx+2cosx at (pi/2, 1) is
A. 2x-y=pi-1 B. 2x+y=pi+1 C. 2x-2y=2-pi D. 4x+2y=2-pi I got A

Answers

lo que queres es 34 5 5 5

Solve -23.7 + d = -48.57.

-4.62
-46.2
-24.87
-72.27

Answers

[tex]-23.7+d=-48.57[/tex]
isolate the variable by adding 23.7 [tex]-23.7+d+23.7=-48.57+23.7[/tex]
[tex]d=-48.57+23.7=-24.87[/tex]

Answer:-24.87 is the correct answer, i checked it!

Step-by-step explanation:

Solve the inequality 2x - 3 < x 2 ≤ 3x 5. show your work

Answers

Answer:

-3/2 ≤ x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x+5

Solve the inequality separately

2x-3 <x+2 and x+2≤ 3x+5

LEts solve one by one

2x-3 <x+2

Subtract x from both sides

x -3 < 2

add 3 on both sides

x< 5

x+2≤ 3x+5

Subtract 3x from both sides

-2x + 2 ≤ 5

Subtract 2 from both sides

-2x ≤ 3

Divide both sides by -2

x ≥ -3/2

we got x>= -3/2 and x<5

so x lies between -3/2 and 5

-3/2 ≤ x < 5

The solution to the given inequality is -3/2 ≤ x < 5.

To solve the given inequality: 2x - 3 < x + 2 ≤ 3x + 5, we can break it down into two separate inequalities and solve them individually.

2x - 3 < x + 2:

Subtracting x from both sides:

2x - x - 3 < x - x + 2

x - 3 < 2

Adding 3 to both sides:

x - 3 + 3 < 2 + 3

x < 5

Now x + 2 ≤ 3x + 5:

Subtracting x from both sides:

x - x + 2 ≤ 3x - x + 5

2 ≤ 2x + 5

Subtracting 5 from both sides:

2 - 5 ≤ 2x + 5 - 5

-3 ≤ 2x

Dividing both sides by 2:

-3/2 ≤ x

Combining the results from both inequalities:

-3/2 ≤ x < 5

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A common rule is that housing expenses should not be more than 28% of your monthly income. Your monthly income is $3,200. How much can you spend on housing?

Answers

About 1,000 is the answer

Answer:

less than $896.00

Step-by-step explanation:

A common rule is that housing expenses should not be more than 28% of your monthly income.

your monthly income = $3,200

so your housing expense should not be more than 28% of $3,200

= [tex]\frac{28}{100}[/tex] × 3,200

= 0.28 × 3,200 = $896.00

So you can spend less than $896.00 on housing expenses.

Other Questions

Is my answer correct? Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).

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Is my answer correct?
Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).