Exponential Growth and Decay
Name ________________________________
Identify each as growth or decay.
1.
2.
a) growth
b) decay
x
0
1
2
3
4
y
125
25
5
1
0.2
a) growth
b) decay
3.
Growth or decay?
Growth or decay?
Factor:
Factor:
Rate:
Rate:
Initial Value:
Initial Value:
5. Given
identify the following:
What is the initial value?
What is the growth/decay factor?
What is the growth/decay rate?
Table #1:
x
-1
0
1
2
3
Table #2:
x
2
3
4
5
6
y
0.5
2
8
32
128
y
4
2
1
0.5
0.25
1. Growth/Decay Factor: ______________
2. Growth/Decay Rate: _______________
3. Initial Value: _____________
4. Write the equation of the exponential function:
5. Growth/Decay Factor: _____________
6. Growth/Decay Rate: ______________
7. Initial Value: ________________
8. Write the equation of the Exponential Function:
7. An initial population of 5 squirrels increases by 9% each year for 10 years. Using x for years and y for
the number of squirrels, write the equation that models this situation.
How many squirrels will there be in 10 years?
8. A car purchased for $34,000 is expected to lose value, or depreciate, at a rate of 6% per year. Using x
for years and y for the value of the car, write the equation that models this situation.
After how many years is the car first worth less than $21,500?
Growth vs. Decay
1. Circle the appropriate description of each graph.
A)
Exponential Growth
Exponential Growth
Exponential Decay
Circle the appropriate description of each equation.
x
5
B) f  x   4  
Exponential Growth
2
Exponential Decay
Exponential Decay
 _
y  .3  .8 
 
x
Exponential Growth
Exponential Decay
Factors, Rates, and Initial Values
2. Given y  1.23x , identify the growth/decay factor, growth/decay rate, and the initial value.
Growth/Decay Factor_________________
Growth/Decay Rate__________________
Initial Value________________________
x
3. Given f  x   3  4  , identify the growth/decay factor, growth/decay rate, and the initial value.
5
Growth/Decay Factor_________________
Growth/Decay Rate__________________
Initial Value________________________
4. Given f  x   0.75  0.60  , identify the growth/decay factor, growth/decay rate, and the initial value.
x
Growth/Decay Factor_________________
Growth/Decay Rate__________________
Initial Value________________________
Equations from Context
5. A Gila Monster is about 16 cm long at birth. During the beginning of its life, the Gila Monster’s length
increases by about 15% each week.
Write a function that models the length of the Gila Monster at the beginning of the Gila Monster’s life
Use x for the number of weeks and y for the length of the Gila Monster.
Find the length of the Gila Monster at the end of the 3 weeks.
6. Sam takes an 800 mg Ibuprofen for her nagging backache. Every hour that the Ibuprofen is in her
system, a quarter of the medicine dissolves in her body. (These are made up facts. Always consult your
physician or pharmacist before taking medication)
Write a function that models the amount of Ibuprofen in Sam’s body over time
Use x for hours, and y for the amount of Ibuprofen, in mg, remaining in the body.
When there is less than 200mg of medicine left in the body, it is safe to take it again. How long will
it take before Sam can take more medicine?
Equations from Tables
7. Write an exponential function that models the points in the table.
X
Y
1
2
3
4
80
20
5
1.25
X
Y
1
2
3
4
-3
-9
-27
-81