AFM Name______

Applications of Exponential Functions

Practice 2

1.  Explain the difference between linear and exponential growth. That is, without writing down any formulas, describe how linear and exponential functions progress differently from one value to the next. Use complete sentences.

2.  A population has size 100 at time t=0, with t in years.

a.  If the population grows by 10 people per year, find a formula for the population, P, at time t.

b.  If the population grows by 10% per year, find a formula for the population, P, at time t.

c.  Graph both functions on the same axes and sketch the graph from the calculator in the given box. Be sure to label your window.

3.  A population has size 5000 at time t=0, with t in years.

a.  If the population decreases by 100 people per year, find a formula for the population, P, at time t.

b.  If the population decreases by 8% per year, find a formula for the population, P, at time t.

4.  The following formulas give the populations (in thousands) of four different cities, A, B, C, and D. Which are changing exponentially? Describe in words how each of these populations is changing over time.

The tables in problems 5 – 6, contain values from an exponential or a linear function. In each problem:

a.  Decide if the function is linear or exponential.

b.  Find a possible formula for each function by hand.

5. 

x / f(x)
0
1
2
3
4 / 12.5
13.75
15.125
16.638
18.301

6. 

x / f(x)
0
1
2
3
4 / 0
2
4
6
8

In problems 7 – 10, is the function linear or exponential or is it neither? Write possible formulas for the linear or exponential functions using the regression capabilities of the calculator.

r / 1 / 3 / 5 / 7 / 9
p(r) / 13 / 19 / 25 / 31 / 37

7.

t / 1 / 2 / 3 / 4 / 5
g(t) / 512 / 256 / 128 / 64 / 32

8.

11.  Let P(t) be the population of a country, in millions, t years after 2002, with P(7)=3.21 and P(13)=3.75.

a.  Find a linear formula for P(t). Describe in words the country’s annual population growth.

b.  Find an exponential formula for P(t). Describe in words the country’s annual population growth.

12.  The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N represent the number of asthma sufferers (in millions) worldwide t years after 1990.

a.  Write N as a linear function of t.

i.  What is the slope?

ii. What does it tell you about asthma sufferers?

b.  Write N as an exponential function of t.

i.  What is the growth factor?

ii. What does it tell you about asthma sufferers?

c.  How many asthma sufferers are predicted worldwide in the year 2010 with the linear model?

d.  With the exponential model?