Question

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

Answer 1

To make the function a decay function the rate of change in the function A(x) is r<0.

Explanation:

Given : The exponential function
`A(x)=P(1+r)^x`

To find : What value for r will make the function a decay function?

Solution :

The exponential function is
`A(x)=P(1+r)^x`,

where, P is the initial value

and r is the rate of change

The condition of rate of change is

1) The function is an exponential growth if their is positive rate of change i.e r>0.

2) The function is an exponential decay if their is negative rate of change i.e. r<0.

Therefore, To make the function a decay function the rate of change in the function A(x) is r<0.

Answer 2

The function will be a decay function for
.. |1 +r| < 1
.. -1 < 1 +r < 1
.. -2 < r < 0

Any value of r in the interval (-2, 0) will make the function a decay function.

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If x can have non-integer values, then you probably want r ∈ (-1, 0).