Question

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 2025. (Round your answers to three decimal places.)

2020 | P = |
thousand people |

2025 | P = |
thousand people |

(c) According to the model, during what year will the population
reach 210,000?

Answer #1

This exercise deals with data from the U.S. Bureau of the Census
on populations of major cities.† These data allow us to find how
fast the population is growing and when it will reach certain
levels. Such calculations are very important, because they indicate
the future needs of the population for goods and services and how
well the area can support the population.
The third largest city in the United States is Chicago. Its
population in 2011 was 2,705 (in...

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)...

Given the following data:
Year
t=0 in 1970
Population (thousands)
1970
0
225.3
1977
7
301.1
1989
1995
365.5
427.6
2000
495.6
Using t = 0 in 1970, write a
linear model using the information from 1989 and 2000.
(This is what we did earlier—use two
points to calculate slope and y intercept)
_________________________
B. Write the linear
regression equation. (Use your calculator)
_________________________
C.
Using the regression equation,
predict when the population will...

a. Develop the model that represents the population of
Chicago
b. predict the population in 2019
c. predict the population in 2024
d. predict when the population will be double its 2011
population
Relates to this question:
Exercise 5-12 deal with data from the U.S. Bureau of the Census
on populations of major cities. These data allow us to find how
fast the population is growing and when it will reach certain
levels. Such calculations are very important, because they...

Consider this scenario: The population of a city increased
steadily over a ten-year span. The following ordered pairs show the
population x and the year y over the ten-year
span in the form (x, y) for
specific recorded years. Use linear regression to determine a
function y, where the year depends on the population.
Round to three decimal places of accuracy.
(2500, 2001), (2650, 2002), (3000, 2004), (3500, 2007), (4200,
2011)
Predict when the population will hit 13,000.
The linear...

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...

A sociologist is interested in the relation between x =
number of job changes and y = annual salary (in thousands
of dollars) for people living in the Nashville area. A random
sample of 10 people employed in Nashville provided the following
information.
x
(number of job changes)
4
3
5
6
1
5
9
10
10
3
y
(Salary in $1000)
38
34
31
32
32
38
43
37
40
33
In this setting we have ?x = 56,...

The cost of a daily newspaper varies from city to city. However,
the variation among prices remains steady with a population
standard deviation of $0.20. A study was done to test the claim
that the mean cost of a daily newspaper is $1.00. Thirteen costs
yield a mean cost of $0.95 with a standard deviation of $0.18. Do
the data support the claim at the 1% level?
Note: If you are using a Student's t-distribution for the
problem, you may...

On a typical night in a large city, about 25,000 people attend
a theatrical event, paying an average cost of over $110 per
ticket. The results of a multiple regression of weekly data for the
receipts in millions of dollars, the paid attendance in
thousands, the number of shows, and the average ticket price are
found below.
Write the regression model.
Receipts = −17.0253 + 0.1116 Attendance + 0.0071 # Shows +
0.2016 Price
1.What does the coefficient of Attendance...

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