Question

Given the exponential function A(x) = P(1 + r)x, what value for r will make the function a growth function?

Answer 1

The value of r has to be greater than 0. r>0

Answer 2

The function is a growth function when
`r>0`.

Explanation:

We are given,

The exponential function is
`A(x)=P(1+r)^x`, where P= initial value and r= rate of change.

Now, we know,

1. The function is an exponential growth if their is positive rate of change.

2. The function is an exponential decay if their is negative rate of change.

Since, it is required to make the function a growth function.

We need the positive rate of change for the function A(x),

That is,
`r>0`

Hence, the function is a growth function when
`r>0`.