Question

Which is an exponential decay function?

Answer 1

Explanation:

An exponential function of the form will decay if

This implies that option A will not decay because

Option B will not decay because which implies that

Option C can be rewritten to get: ....This exponential function decays.

Option D will not decay because

Explanation:

Answer 2

`f(x)=(3)/(2)((8)/(7))^(-x)`

Step-by-step explanation:

An exponential function of the form
`f(x)=a(b)^x` will decay if
`0\:<\:b\:<\:1`

This implies that option A will not decay because
`(7)/(4)\:>\:1`

Option B will not decay because
`f(x)=(2)/(3)((4)/(5))^(-x)\implies f(x)=(2)/(3)((5)/(4))^(x)` which implies that
`b=(5)/(4)\:>\:1`

Option C can be rewritten to get:
`f(x)=(3)/(2)((8)/(7))^(-x)\implies f(x)=(3)/(2)((7)/(8))^(x)`....This exponential function decays.

Option D will not decay because
`-(9)/(2)\:<\:0`