Find The Inverse Of The Function

Question

A(t)=500(1/2)^t/272

I found the inverse by using MathWay and my teacher says its wrong

"Please write this with a log base of 1/2. Also this is not an equation as you have it written. It needs to have the right variables as well."

Please Help

Answer 1

A(t) = 500(0.5)^t/272

A(t) / 500 = (0.5)^t/272

ln [A(t) / 500] = ln [(0.5)^t/272]

ln [A(t) / 500] = (t/272) ln 0.5

272 [ln A(t) - 500] = t ln 0.5

272 [ln A(t) - 500] / ln 0.5 = t

Answer 2

To find the inverse, we first exchange variables A and t:

t = 500(1/2)^(A/272)

and relabel A by A^-1 (because this will be the inverse function).

Now, take log_1/2 of both sides:

log_1/2t = log_1/2500 + log_1/2(1/2)^(A^-1/272) = log_1/2500 + A^-1/272

Solving for A^-1 gives:

A^-1(t) = 272*log_1/2(t/500).