# Exponentials

EXPONENTIAL FUNCTIONS
NAME______________________________
1. Linear and exponential functions have very unique properties. Write a paragraph explaining these
properties. Include how you can determine if data follows a linear pattern or an exponential pattern.
2. Determine which table illustrates an exponential function and which one illustrates a linear function.
Find formulas for these two functions.
x f ( x)
-2 -25.22
0
3.50
2 32.22
4 60.94
6 89.66
x
0.5
1
2
4
8
x
-3
-1
1
3
5
g ( x)
-1
0
1
2
3
h( x )
1.3310
1.9167
2.7600
3.9744
5.7231
3. Determine which situation is linear and which is exponential. Find a formula for each.
A computer purchased for \$3200 loses roughly 20% of its value each year.
A kitchen appliance purchased for \$120 loses roughly \$18 in value every two years.
4. Find a formula for each graph.
A. Contains the points (0,1.5) and (2,0.4374)
15
10
5
0
-2
-1
0
1
x
2
3
B. Contains the points (-2,0.48) and (2,18.75)
50
40
30
20
10
0
-2
-1
0
1
2
3
x
C. An exponential function passing through (0,0) and (1,5.18) with a horizontal asymptote of y  7 .
5. In 1994, a reporter from the local news station said that the population of Arizona would double by
2015. From this information, determine the annual growth rate and the monthly growth rate.
6. The number of people who hear a rumor tends to follow a saturated growth curve. Suppose a
particular town has 2000 people. Three days after a rumor is introduced, 140 people will have
heard it. Use a saturated growth curve to determine when half the town will have heard the rumor.