Question

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

Answer 1

ANSWER
Any value of r in between -1 and 0 (exclusive on both sides).
For example, r = -0.1 or r = -0.5

EXPLANATION
You did not specify any answer choices; all we can do is state a range of values for r.

We have exponential function $A(x) = P(1 + r)^x$

We note that the base is "1 + r"

For an exponential function to be a decay function, the base must be between 0 and 1 exclusive.

   $\begin{array}{r c c c l l} 0 &\ \textless \ & 1 + r &\ \textless \ & 1 \\ -1 &\ \textless \ & r &\ \textless \ & 0 & (\text{\footnotesize Solve for r by subtracting 1 from everything}) \end{array}$

Therefore, the values for r must lie in the range -1 < r < 0 (between -1 and 0 exclusive)

In interval notation, this is expressed as (-1, 0)