Question

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?

Answer #1

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.

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,...

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?

The population of the world was about 5.3 billion in 1990 (t =
0) and about 6.1 billion in 2000 (t = 10). Assuming that the
carrying capacity for the world population is 50 billion, the
logistic differential equation
dP =kP(50−P)dt
models the population of the world P(t) (measured in billions),
where t is the number of years after 1990. Solve this differential
equation for P(t) and use this solution to predict what the
population will be in 2050 according...

The following table shows the population in a town in the given
year.
Year
1960
1970
1980
1990
2000
Population
2005
2549
3100
3670
4010
a) Which is the independent variable? Which is the dependent
variable?
Independent:
_____________
Dependent: _______________
b) Find the percent change in population from 1980 to 1990.
c) Find the average growth rate in population from 1980 to
1990.
d) Use interpolation to estimate the number of people in 1984.
Round...

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 = ?

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...

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...

1. Find a function f given that the slope of the tangent line to
the graph of f at any point P(x, y) is given by y' = − 4xy x2 + 1
and the graph of f passes through the point (2, 1).
2. The world population at the beginning of 1980 (t =
0) was 4.5 billion. Assuming that the population continued to grow
at the rate of approximately 2%/year, find a function
Q(t) that expresses the world...

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