The table gives estimates of the world population, in millions, from 1750 to 2000. year population year population 1750 790 1900 1650 1800 980 1950 2560 1850 1260 2000 6080 (a) use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950. compare with the actual figures
The exponential model provides a reasonable approximation for the world population growth between 1750 and 1800. However, it becomes less accurate for longer time periods due to various factors like technological advancements, medical breakthroughs, and changing social and economic conditions.
1. Define the model:
The general form of an exponential model is:
P(t) = a * b^(t)
where:
P(t) is the population at time t
a is the initial population (at t = 0)
b is the growth factor (greater than 1 for positive growth)
t is the time elapsed (in years, since the initial time)
2. Find the parameters:
We have data for 1750 (t = 0) and 1800 (t = 50):
P(0) = 790 million (initial population)
P(50) = 980 million (population after 50 years)
Using these values, we can solve for a and b:
b = (P(50) / P(0))^(1/t) = 980 / 790)^(1/50) ≈ 1.007
a = P(0) / b^0 = 790 / 1 ≈ 790
3. Predict the population in 1900 and 1950:
Now we can plug the values of a and b into the model to predict the population:
P(150) = 790 * 1.007^(150) ≈ 1912 million (predicted population in 1900)
P(200) = 790 * 1.007^(200) ≈ 3145 million (predicted population in 1950)
4. Comparison with actual data:
The actual population in 1900 was 1650 million and in 1950 was 2560 million. While the model overestimates the population in both cases, it still captures the general trend of growth.
Find the extreme values of f subject to both constraints f(x,y) = 2x^2+3y^2-4x-5, x^2 + y^2 <=16
what is 58/7 as a mixed number
Answer:
[tex]8\frac{2}{7}[/tex] and or 8 2/7
have an amazing day!
Step-by-step explanation:
Simplify the expression
(-5)^3
Answers:
–125
125
–15
25
What is the product in simplest form?(In fractions) -5 1/2*8 1/3
A.-20/39
B.-10/39
C.-5/39
D.3/25
It takes 45 minutes for 4 people to paint 5 walls.
How many minutes does it take 6 people to paint 4 walls
4 people x 45 minutes = 180 minutes total to paint 5 walls
180/5 = 36 minutes of man work per wall
36 * 4 walls = 144 total minutes
144/6 people = 24 minutes total
Jared used one whole number 2/5 of soil for his garden. He is digging another garden that will need 1/5 as much soil as the original. How much will he use total.
Given f(x) = −9x5 − x4 + 3x3 − 8 and g(x) = −9x5 − 3x3 − 9x2 + 7, find and simplify f(x) − g(x)
What reasoning and explanations can be used when solving radical equations?
Answer:
The common reasoning that can be use while solving a radical equation are shown below.
Step-by-step explanation:
Radical equations are the equations which contains radical expressions like [tex]\sqrt{x}\text{ and }\sqrt{x+2}[/tex], etc.
If a radical expression is defined as [tex]\sqrt{x}[/tex], then the sign [tex]\sqrt{}[/tex] is the radical and x is radicand.
The common reasoning that can be use while solving a radical equation are:
1. Isolate or separate the radical expression.
2. To remove radical square both sides of the equation.
3. After that solve the equation to find the unknown variable
4. Check the answer for solution or extraneous solution.
For example:
[tex]\sqrt{x+1}+1=x[/tex]
subtract 1 from both sides.
[tex]\sqrt{x+1}=x-1[/tex]
Taking square on both sides.
[tex]x+1=(x-1)^2[/tex]
On simplification we get
[tex]x+1=x^2-2x+1[/tex]
[tex]0=x^2-2x+1-x-1[/tex]
[tex]0=x^2-3x[/tex]
[tex]0=x(x-3)[/tex]
Using zero product property,
[tex]x=0,x-3=0\Rightarrow x=3[/tex]
Check the equation for x=0,
[tex]LHS=\sqrt{0+1}+1=1+1=2\neq 0=RHS[/tex]
Since LHS is not equal to RHS, therefore 0 is an extraneous solution.
Check the equation for x=3,
[tex]LHS=\sqrt{3+1}+1=2+1=3=RHS[/tex]
Since LHS is equal to RHS, therefore 3 is an solution.
Kevin has three fourths yard of string he uses one third for a school project how many yards of string did he use on the project
_______
hint the answer is not 1/3 or 33.33333333%
3/4 yard,
he used 1/3
3/4 * 1/3 = 3/12 = 1/4
he used 1/4 yard
The skateboard that Jose wants costs $90 has a coupon for 1/5 off retail price. If Jose saves $18 a week, how long will it take to save enough to buy the skateboard?
Answer:
4 weeks
Step-by-step explanation:
write each percent as a fraction 13_1/3
what is the rule for solving proportions? A. The sum of the means is the product of the extremes. B. The product of the means is equal to the product of the extremes. C. The product of the extremes is twice the product of the means.
The rule for solving proportions is that the product of the means equals the product of the extremes. This method is used when dealing with categorical data in two categories.
Explanation:The rule for solving proportions is this: The product of the means is equal to the product of the extremes (option B). When you have a proportion which is often written in the mathematically form 'a/b = c/d', you can use this rule. 'a' and 'd' are the extremes and 'b' and 'c' are the means. Therefore, the rule means that a*d (product of the extremes) is equal to b*c (product of the means).
In terms of identifying when you're dealing with a proportion problem, you're involved in this scenario when the data you're dealing with is of two categories like Yes or No, Success or Failure. This is typically when you're attempting to estimate a population proportion for example, the proportion of the population that smokes or will vote for candidate A.
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-4 4/5 divided by 4 please help!!!!!!
Robin's family breeds Great Danes. In the last litter, one of the puppies grew at an unusually consistent rate. At birth, he weighed two pounds. At eight months, he weighed 110 pounds.
Answer:
A. An additional month of growth is associated with an additional 13.5 pounds of weight.
Step-by-step explanation:
Please help me with this Math question
emma siad "it is seventyfive hundredths of a mile to waterslide park." Charles said "it is seven and five-tenths miles to water slide park." whose statement makes sence?whose statement is nonsense? Explain your reasoning?
Given f(x) = −9x5 − x4 + 3x3 − 8 and g(x) = −9x5 − 3x3 − 9x2 + 7, find and simplify f(x) − g(x)
The total mileage they walked was 16 2/3 miles. If each kid contributed 4 1/6 miles to the hike, how many kids went on the hike?
Answer:58
Step-by-step explanation:
A 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground
We apply the Pythagorean theorem and differentiate it to relate the rates of the ladder's top slipping and the foot of the ladder moving away from the wall. Substituting given values in the differentiated equation gives us the speed at which the foot of the ladder is moving away.
Explanation:In this problem, we are dealing with a right triangle formed by the wall, ground and the ladder acting as the hypotenuse. The rate at which the top of the ladder is descending and the height at which the rate needs to be calculated are given. This problem applies the concepts of related rates in calculus.
According to the Pythagorean theorem, for a right triangle, the sum of the square of the two shorter sides is equal to the square of the longest side (the hypotenuse). Here, we have x² + y² = 15² where x is the distance of foot of the ladder from the wall and y is the height from the ground.
Differentiating both sides with respect to time (t), we get 2x(dx/dt) + 2y(dy/dt) = 0. Solve this differentiation equation to find dx/dt, the speed of the foot of the ladder moving away from the wall while y is 13.
To solve this, plug y = 13, dy/dt (rate at which top of ladder is descending) = -4 ft/sec into the equation and solve for dx/dt.
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What is the solution to 3/4(x+8)=9
rounded to hundred how can I round to hundred
9,032,504.75 in word form
A train is traveling from New Orleans to Memphis at a constant speed of 79 mph New Orleans and Tennessee are 395.1 miles apart how long will the train take to Tennessee
Answer:
About 5.0 hours
Step-by-step explanation:
The observations you made in the unit circle can help you determine the x‑ and y‑coordinates of special points on the circle without memorizing the circle. Analyze some of the patterns by completing the parts below.
a. Look at all the ordered pairs whose angles are of the form k pi/4, where k is an integer. What do you notice?
b.Now look at the ordered pairs whose angles are of the form k pi/6 or k pi/3. What do you notice about their coordinates?
c.How can you determine if the coordinates of a point are positive or negative?
A nationwide survey of college seniors by the university of michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in parade. if 12 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is
a. anywhere from 7 to 9;
b. at most 5;
c. not less than 8.
Suppose x and y vary together such that x is 7 times as large as y. write a formula that defines x in terms of y.
In 2001, the United States' oil consumption was 7,297.4 millions of barrels, while Japan's was 1,979.4 millions of barrels. How many more barrels did the United States consume than Japan?
Po is trying to solve the following equation by completing the square: 49x^2+56x-64 = 0.He successfully rewrites the above equation in the following form: (ax + b)^2 = c,where a, b, and c are integers and a > 0. What is the value of a + b + c?
Halp
To solve the equation 49x²+56x-64 = 0 by completing the square, we first convert it to the format (ax + b)² = c. It is found that a=1, b=4/7, and c=16/49. Hence, a+b+c = 381/147 or approximately 2.59183673469.
Explanation:The equation to solve is 49x²+56x-64 = 0. By completing the square, we can rewrite the equation in the form (ax + b)² = c. To get to this form, Po first divided the entire equation by 49, giving x²+8/7x-64/49= 0. Following this, he then took half of the coefficient of x (which is 4/7), squared it (which is 16/49), and added it to both sides of the equation. This transforms the left-hand side of the equation into a perfect square giving us (x+4/7)²=16/49. Hence, we find that a=1, b=4/7, and c=16/49. Therefore a+b+c = 381/147 or approximately 2.59183673469.
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What is the product?
(4x)(-3x8) (-7x3)
Answer: [tex]84x^{12}[/tex]
Step-by-step explanation:
The given expression : [tex](4x)(-3x^8) (-7x^3)[/tex]
Open brackets, we get
[tex]4x\cdot-3x^8\cdot-7x^3\\\\=4\cdot-3\cdot-7\cdot x\cdot x^8\cdot x^3[/tex]
Using law of exponents:-
[tex]a^m\cdot a^n=a^{m+n][/tex]
[tex]84\cdot x^{1+8+3}\\\\=84x^{12}[/tex]
Hence, the product [tex](4x)(-3x^8) (-7x^3)=84x^{12}[/tex]
Answer:
C. 84X^12
Step-by-step explanation:
edge 2021