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

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.

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

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?

Some examples that follow the law of uninhibited growth:

-interest compounded continuously

(A = Pert)

-cell and bacterial growth

- population growth

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.

N(t) = 100e0.045t

a) Determine the initial amount of bacteria

N(t) = 100e0.045t

b) What is the growth rate of the bacteria?

N(t) = 100e0.045t

c) Graph the function using a graphing utility

N(t) = 100e0.045t

d) What is the population after five days?

N(t) = 100e0.045t

e) How long will it take for the population to reach 140 grams?

N(t) = 100e0.045t

f) What is the doubling time for the population?

Ready to try some problems?

Homework: p. 334/ 1-4