Question

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

r = 2.1
r = −0.1
r = 0
r = 0.1

Answer 1

Option 2nd is correct

-0.1 value for r will make the function a decay function

Explanation:

An exponential decay function is given by:

`y = a(1-r)^x`

where,

a>0 is the initial value,

r rate of decrease (0<r < 1) and

x is the time

As per the statement:

Given the exponential function

`A(x) = P(1 + r)^x`

from the given options and by definition, we have;

r = -0.1

Therefore, -0.1 value for r will make the function a decay function

Answer 2

Any negative value of r will make the sum 1+r be less than 1.

The appropriate choice is r = -0.1.