Think about a quantity that under specific conditions increases by a fixed percentage during constant periods of time.
B
b
Think about a quantity that under specific conditions decreases by a fixed rate during constant periods of time.
A
a
Example application: Compound interest
B
b
Example application: Radioactive decay
Practice makes perfect
a
Exponential growth functions can be used to model compound interest. This occurs when you have savings in a bank account and you leave the money long enough that the annual interest rate applies consecutively. For example, a bank account with 10 % annual interest rate can be modeled by the function shown below.
y = 100(1.1)^x
In this function, 100 represents the initial amount of money. For example, $100.
This function is a good example of exponential growth rate since it is increasing by a constant 10 % each time x increases by 1.
b
Exponential decay functions can be used to model radioactive decay. This occurs when unstable atoms disintegrate, emitting energy. For example, a radioactive element with a half-live of 1 hour can be modeled using the function shown below. The half-live of a radioactive element is the tame it takes to disintegrate to half of its original quantity.
y=400(0.5)^x
In this function, 400 represents the initial quantity. For example, 400 grams.
This function is a good example of exponential decay, since it is decreasing by a constant 50 % each time x increases by 1.
