1. Exponential Growth and Decay
We’ve had some experience dealing with exponential functions, but this chapter takes what we know and puts it in a real-world context

2. Exponential growth and decay are rates; that is, they represent the change in some quantity through time. Exponential growth is any increase in quantity over time, while exponential decay is any decrease in quantity over time.

3. N(t) = N0ekt (exponential growth) or N(t) = N0e-kt (exponential decay)
where:
N0 is the initial quantity
t is time
N(t) is the quantity after time t
k is a constant not equal to zero, and
ex is the exponential function

4. Can you think of a familiar example?
Exponential growth is also called the Law of uninhibited growth, and can be used with any variable for your initial and ending quantities.
For example :
A = A0ekt
Can you think of a familiar example?

5. Some examples that follow the law of uninhibited growth:
interest compounded continuously
(A = Pert)
cell and bacterial growth
- population growth

6. Let’s go through an example:
A colony of bacteria grows according to the law of uninhibited growth according to the function N(t) = 100e0.045t, where N is measured in grams and t is measured in days.

7. a) Determine the initial amount of bacteria
N(t) = 100e0.045t
a) Determine the initial amount of bacteria

8. b) What is the growth rate of the bacteria?
N(t) = 100e0.045t
b) What is the growth rate of the bacteria?

9. c) Graph the function using a graphing utility
N(t) = 100e0.045t
c) Graph the function using a graphing utility

10. d) What is the population after five days?
N(t) = 100e0.045t
d) What is the population after five days?

11. e) How long will it take for the population to reach 140 grams?
N(t) = 100e0.045t
e) How long will it take for the population to reach 140 grams?

12. f) What is the doubling time for the population?
N(t) = 100e0.045t
f) What is the doubling time for the population?

13. Ready to try some problems?
Homework: p. 334/ 1-4