Question

An exponential function is expressed in the form y= ab^x. This relation represents a growth when ____ and a decay when ______.

Answer 1:

- b>1
- 0 - b is positive
- b is negative
- a > 1
- 0
Answer 2:

- b>1
- 0 - b is positive
- b is negative
- a > 1
- 0

Answer 1

This relation represents a growth when b > 1 and a decay when b < 1.

Explanation:

The previous value of y is multiplied by b when x increases by 1. In order for the product to be greater than the previous value (growth), the value of b must be greater than 1.

In order for the product to be smaller than the previous value (decay), the value of b must be less than 1.

_____

Comment on the nature of the function

In order for the function value to remain positive, both "a" and "b" must be greater than zero.