Question

Which is a stretch of an exponential decay function?

Answer 1

The correct option is C. The function
`f(x)=(5)/(4)((4)/(5))^x` is a stretch of an exponential decay function.

Explanation:

The general form of an exponential function is

`f(x)=ab^x`

where, a is the initial value and b is the growth factor.

If b<1, then it represents a decay function and if b>1, then it represents a growth function.

Let k be a stretch and compression factor.

`g(x)=kf(x)`

If k<1, then it represents vertical compression and if k>1, then it represents vertical stretch.

In third function

`f(x)=(5)/(4)((4)/(5))^x`

`k > 1`

`b < 1`

Therefore the function
`f(x)=(5)/(4)((4)/(5))^x` is a stretch of an exponential decay function.