Question

Given an exponential function for compounding interest, A(x) = P(.95)x, what is the rate of change?

−0.05%

−95%

−5%

95%

Answer 1

Option 3

The rate of change is -5%

Explanation:

Given : An exponential function for compounding interest,
`A(x) = P(.95)^x`

To find : What is the rate of change?

Solution :

The general form of an exponential function is:

`f(x) = a(1+r)^x`

Where, a is the initial amount,

(1+r) is the rate of change,

r is the growth or decay factor

We have given,
`A(x) = P(.95)^x`

Rate of change is

`1+r=0.95`

`r=0.95-1`

`r=-0.05`

Convert to percent,

`r=-0.05* 100=-5\%`

Therefore, Option 3 is correct.