Chapter 1 - Worksheet 2 - EXPONENTIAL FUNCTIONS
Place answers on this sheet. Show work on your own paper.
NAME________________________________
1. Determine which table illustrates an exponential function and which one illustrates a linear function. Find
formulas for these two functions. Then find a formula for the third function. Show work.
x
f ( x)
x
h( x )
-2
0
2
4
6
-25.22
3.50
32.22
60.94
89.66
-3
-1
1
3
5
1.3310
1.9167
2.7600
3.9744
5.7231
Constant slope so linear
constant ratio so exponential
h( x)  2.3(1.2) x
f ( x)  14.36 x  3.5
Common ratio is 1.44 and x values are 2 apart
so b 2  1.44  b  1.441 / 2  1.2
2. 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.
Exponential and V (t )  3200(0.80) t
A kitchen appliance purchased for $120 loses roughly $18 in value every two years.
Linear and V (t )  120  9t
3. Find a formula for each graph.
A. Contains the points (0, 1.5) and (2, 0.4374)
B. Contains the points (-2, 0.48) and (2, 18.75)
60
50
40
y
30
20
10
0
-2
-1
0
1
2
3
x
18.75
0.48
Given vertical intercept so a (leading coefficient) = 1.5
Points are 4 units apart so base: b 4 
0.4374
 0.2916  b  0.54
1.5
Equation: f ( x)  1.5(0.54) x
 39.0625  b  2.5 and leading coefficient is 3
and base: b 2 
Equation: f ( x)  3(2.5) x
4. It is predicted that the population of a particular state in 2005 will double by the year 2024. Determine the annual,
monthly, and continuous growth rates.
Doubling time means in equation P(t )  P0 a t , P(19)  2 P0  2 P0  P0 a 19  2  a 19  a  21 / 19
 a  1.0372
So equation is P (t )  P0 (1.0372) t which tells us the annual rate is 3.72%
To find monthly rate: 1.03721 / 12  1.003. So monthly rate is 0.3%
To find continuous rate: e r  1.0372  r  ln 1.0372  0.0365. So the continuous rate is 3.65%
5. A saturation curve passing through (0,0) and (1,5.18) with a horizontal asymptote of y  7 .
(Hint: hint 1.2 and/or example in textbook in 1.2 Saturation Curve)
Since horizontal asymptote is y  7 is S. 5.18  7(1  a1.5 )  a  0.26
Equation is f ( x)  7(1  0.26 x )  7(1  e 1.347 x )
6. The number of people who hear a rumor tends to follow a saturated growth model.
Suppose a particular town has 2000 people. Three days after a rumor is introduced, 140 people will have heard it.
Determine when half the town will have heard the rumor.
Since the town has a population of 2000 people that tells us that the horizontal asymptote is y  2000.
140  2000(1  a 3 )  a 3  0.93  a  0.9761
So the equation is R(t )  2000(1  0.9761t )  2000(1  e 0.02419t )
To find when half the town has heard: 1000  2000(1  0.9761t ) 
1
 0.9761t  t  28.654 days
2