Find the inverse of this function....?

Question

Q(t) = M(1 - e^ (-t/a))

Answer 1

what grade are you in???

Answer 2

y = (3 + e^x) / (3 - e^x)

y+1=6/(3 - e^x)

y-1=2e^x/(3 - e^x)

(y-1)/(y+1)=1/3 e^x

x=ln|3(y-1)/(y+1)|

then

inv y = ln|3(x-1)/(x+1)|

Answer 3

t= M(1-e^(-y/a))

t/M= 1-e^(-y/a)

-t/M+1= e^(-y/a)

ln (-t/M+1)= ln e^(-y/a)

ln (-t/M+1)= -y/a

-a ln (-t/M+1)= y

Inv Q(t)= -a ln (-t/M+1)

x= (3+e^y) / (3-e^y)

x(3-e^y)= (3+e^y)

ln (x(3-e^y))= ln (3+e^y)

ln 3x-ln xe^y= ln 3+ln e^y

ln 3x-ln xe^y= ln 3+y

ln 3x-(ln x)(ln e^y)= ln 3+y

ln 3x-y(ln x)= ln 3+y

ln 3x-ln 3= y(ln x)+y

ln 3x-ln 3= y(ln x+1)

(ln 3x-ln 3)/(ln x+1)= y

Inv y= (ln 3x-ln 3)/(ln x+1)