5.15.4 • Comparing Linear and Exponential Growth
Cool Down
The linear function is defined by .
a. Show that and have a difference of 4.
b. Show that when the input value increases from to , the output values and have a difference of 4.
Compare your answer:
a.
- , and . The difference of 12 and 8 is 4.
b. , which equals 4.
The exponential function is defined by .
a. Show that and have a quotient of 4.
b. Show that when the input value increases from to , the output values and have a quotient of 4.
Compare your answer:
a.
- , and . The quotient is , which is 4.
b. , which equals 4.
Why Should I Care?
Exponential models can help you understand the power of investment. After two years, this investor made $210 off of an initial investment of $1000 because of the 10% interest rate.
Can you calculate how much money the investor will have made after twenty years?