inverse functions?

Question

q(t) = q0[1-e^(-t/a)] q0 being a variable.

inverse i got t/[1-e^(-t/a)] = q0 and then I replace the t's with q0? Thanks!

Answer 1

q(t) = q0(1 - e^(-t/a))

t = q0(1 - e^(-q(t)/a))
t/(q0) = 1 - e^(-q(t)/a)
(t/(q0)) - 1 = -e^(-q(t)/a)
-(t/(q0)) + 1 = e^(-q(t)/a)
ln((-t/(q0)) + 1) = (-q(t))/a
aln((-t/(q0)) + 1) = -q(t)
-a * ln((-t/q0) + 1) = q(t)

ANS : q^-1(t) = -a * ln((-t/(q0)) + 1)

Answer 2

In Algebra II inverses are found by switching the 2 variables then solving for the one originally by itself ( q(t) in yours). Are a and t constants? I think they'd have to be if this is a function. Try writing q0 = qt [ .... ] and solving for qt. Butr this could be totally inappropriate for your level math.