Question

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*
b^{t} ) that relates P(t) and t. Round the value of b to 5
significant figures.

a = ?

b = ?

Answer #1

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 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)...

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?

A
town's population has been increasing. In 2001 the population was
38000 people. By 2011 the population had grown to 45000 . A write
an equation that models this situation. Let p(t)=mt +b be the form
. B) how many people will be living in the town by 2018? C) when
will the population reach 100000 people at this rate? Round to the
nearest year?

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...

Exponential Model: P(t) = M(1 − e^−kt) where M is maximum
population.
Logistic Model: P (t) = M / 1+Be^−MKt where M is maximum
population.
Scientists study a fruit fly population in the lab. They
estimate that their container can hold a maximum of 500 flies.
Seven days after they start their experiment, they count 250
flies.
1. (a) Use the exponential model to find a function P(t) for the
number of flies t days after the start of the...

Suppose the town of Boone has a total population of 70,000
people. Of those, 65,000 people are employed. There are 1,000
full-time students who are not employed or actively seeking work.
The rest of the people are out of work but have been actively
seeking work within the past four weeks.
Instructions: In part a, round your answer to 1
decimal place. In part b, enter your answer as a whole number.
a. What is Boone’s unemployment rate?
percent
b....

Suppose you were hired on January 1, 2010 and started depositing
$200 at the end of each month, with the first deposit on January
31, 2010, in a pension fund that pays interest of 9% per year
compounded monthly on the minimum monthly balance and credited at
the end of each month.
(a) How much money was in the pension fund on February 1,
2010?
(b) How much money was in the pension fund on March 1, 2010?
(c) How...

KEY
Region 1 = NW Population 1 = Under 50,000
Region 2 = SW Population 2 = 50,000 - 100,000
Region 3 = NE Population 3 = Over 100,000
Region 4 = SE
Count of Population
Region
Total
population
1
2
3
4
1
34
38
34
38
144
2
36
55
27
33
151
3
35
37
35
48
155
Total :
105
130
96
119
450
Big Burger is a fast food restaurant that has 450 locations all...

On January 1, 2010, the Felix Company purchased a machine to
use in the manufacture of its product. The invoice cost of the
machine was $260,000. At the time of acquisition, the machine had
an original estimated useful life of 10 years and an estimated
salvage value of $20,000. Annual depreciation was recorded at
$24,000 per year. The machine was depreciated using the
straight-line method.
On August 1, 2015, Felix exchanged the old machine for a newer
model. The new...

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