Question

Solve the given problem related to population growth.

A city had a population of 23,100 in 2000 and a population of
26,000 in 2005.

(a) Find the exponential growth function for the city. Use
*t* = 0 to represent 2000. (Round *k* to five decimal
places.)

*N*(*t*) =

(b) Use the growth function to predict the population of the city
in 2015. Round to the nearest hundred.

Answer #1

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...

3.) Starting with the expression for logistic population growth,
determine the expression for the time t1 that it takes for
population to grow from No to N1. Express your answer in terms of
four variables only: r, K, No, and N1.
4.)The rate of growth of a population is given by dN/dt = 100t.
If the total population at t = 10 years is 6000 people, find the
population at t = 20 years. This distribution is NOT exponential or...

In this problem, you will solve for the equilibrium population
of an idealized city experiencing rural-urban migration, following
the augmented Harris- Todaro model from Chapter 3. The incomes
earned in urban employment and in the rural area are y and
yA, respectively, and t is commuting cost per
mile. J is the number of available urban jobs.
a) Suppose the city is a rectangle 10 blocks wide with the
employment center at one end (it’s an island like Manhattan). The...

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 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.
(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...

5. James wants to invest $85000. He can invest the money at 7.3%
with interest compound monthly for 30yr or he can invest at 7.1%
with interest compounded continuously for 30yr. Which option
results in more total interest? Show your work
10. Solve the problem. The population of a country is modeled by
the function P(t) = 17.9e 0.01264t where P(t) is the population (in
millions) t years after January 1, 2000. Use the model to predict
the year during...

Population Growth and Value Decline
Mini-projects are designed to critically stretch your
thinking, let you explore the concept, or make you look at a
specific situation or related problem. By nature, they are more
difficult than the regular exercises.
Problem:: The number of Starbucks stores grew after they first
opened. The number of stores from 1990-2011, as reported on their
corporate website is shown in the chart below..
Carefully plot the data. You should be able to see that the...

This is a challenging multi-step problem. Solve it on paper,
writing out each step carefully. When doing calculations, do not
round intermediate values. Note: If you have approached the problem
in a principled way, do not abandon your approach if your numerical
answer is not accepted; check your calculations! A particular solid
metal has a Young's modulus of 20 × 10^10 N/m2; the mass of one
mole of this metal is 59 g. Assume that in this metal the
interatomic...

In this exercise, you will analyze the supply-demand equilibrium
of a city under some special simplifying assumptions about land
use. The assumptions are: (i) all dwellings must contain exactly
1,500 square feet of floor space, regardless of location, and (ii)
apartment complexes must contain exactly 15,000 square feet of
floor space per square block of land area. These land-use
restrictions, which are imposed by a zoning authority, mean that
dwelling sizes and building heights do not vary with distance to...

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