Without graphing, determine whether the function y=7(2/3)^x represents exponential growth or exponential decay. Explain your answer.

Answer 1

Given: y = 7(2/3)^x

Without graphing, does it represent

exponential growth or dacay?

SOLUTION:

It represents exponential decay.

because the growth factor is (2/3) which is less than 1.

If you keep multiplying a number by a number, less than 1,

then it will keep getting smaller, and smaller.

An easy way to see this is if the growth factor is 1

Then it's like multiplying a number by 1, over and over.

In this case, the number doesn't change.

If the growth factor is > 1

Then when you multiply a number by it,

the product is greater than the original number.