Question

In 2000, the population of Montrose, GA was 153. By 2010, the population had increased to 215. (a) Find the linear model L(t) that gives the population of Montrose t years after 2000. (b) Find the exponential model E(t) that gives the population of Montrose t years after 2000. (c) What do each of the models predict that the population of Montrose will be by 2020?

Answer #1

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Requirement 1a.
A.
In 2000, the population of a country was approximately 5.63
million and by 2060 it is projected to grow to
11 million. Use the exponential growth model
A=A0 ekt
in which t is the number of years after 2000 and A0
is in millions, to find an exponential growth function that models
the data.
B.
By which year will the population be 7 million?
Requirement 1b.
The exponential models describe the population of
the indicated country, A,...

The population of a country on January 1, 2000, is 16.8 million
and on January 1, 2010, it has risen to 18 million. Write a
function of the form P(t) = P0e rt to model the population P(t) (in
millions) t years after January 1, 2000. Then use the model to
predict the population of the country on January 1, 2016. round to
the nearest hundred thousand.
A) P = 16.8e0.00690t; 86.5 million
B) P = 16.8e0.00690t; 18.8 million
C)...

The population of a town was 2350 in 1980. In 2000, the
population was 2550. Find an exponential equation, P(t) that models
this situation, where P is the population and t is the number of
years since 1980. Also, in approximately how many years will the
town’s population reach 3000?

Suppose the population of a town was 40,000 on January 1, 2010
and was 50,000 on January 1, 2015.
Let P(t) be the population of the town in thousands of
people t years after January 1, 2010.
(a) Build an exponential model (in the form P(t) =
a*bt ) that relates P(t) and t. Round the value
of b to 5 significant figures.
(b) Write the exponential model in the form P(t) =
a*ekt. According to this model, what is...

Suppose the population of a town was 40,000 on January 1, 2010
and was 50,000 on January 1, 2015. Let P(t) be the
population of the town in thousands of people t years
after January 1, 2010.
Build an exponential model (in the form P(t) = a
bt ) that relates P(t) and t. Round the value of b to 5
significant figures.
a = ?
b = ?

The population of a region is growing exponentially. There were
35 million people in 1980 (when t=0) and 70 million people in
1990.
Find an exponential model for the population (in millions of
people) at any time t, in years after 1980. P(t)=
What population do you predict for the year 2000? Predicted
population in the year 2000 = million people.
What is the doubling time? Doubling time = years.

The population of a region is growing exponentially. There were
20 million people in 1980 (when t=0) and 70 million people in 1990.
Find an exponential model for the population (in millions of
people) at any time tt, in years after 1980.
P(t)=
What population do you predict for the year 2000?
Predicted population in the year 2000 = million people.
What is the doubling time?
Doubling time = years.

The population P (in thousands) of a certain city from 2000
through 2014 can be modeled by P = 160.3e ^kt, where t represents
the year, with t = 0 corresponding to 2000. In 2007, the population
of the city was about 164,075.
(a) Find the value of k. (Round your answer to four decimal
places.)
K=___________
Is the population increasing or decreasing? Explain.
(b) Use the model to predict the populations of the city (in
thousands) in 2020 and...

In 2000, China’s GDP was ∙$1.2 trillion and its population was
1,280,429,000. By 2010, its GDP was $5.9 trillion and its
population size was 1,359,821,000. If GDP is used as a measure of
affluence, and technology is held constant, how has China’s impact
changed proportionally during those 10 years? How would this be
different if China’s GDP had not increased?

Tacoma's population in 2000 was about 200 thousand, and had been
growing by about 9% each year. a. Write a recursive formula for the
population of Tacoma b. Write an explicit formula for the
population of Tacoma c. If this trend continues, what will Tacoma's
population be in 2016? d. When does this model predict Tacoma’s
population to exceed 400 thousand?

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