Exponential Growth and Decay
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Transcript of Exponential Growth and Decay
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