Question

Inverse of W(t)=200(1.1-e^-t)? I tried but got stuck...

Answer 1

W(t)=200(1.1-e^-t)
=220-200e^-t
-220=-200e^-t
1.1=e^-t
ln1.1=lne^-t
ln1.1=-t
t=ln(-1.1)

Answer 2

-ln(1.1-.005w) is what my answer sheet sayas?

Answer 3

\[Let \space y = 200(1.1-e^{-t})\]
\[y = 220 - 200e^{-t}\]
\[200e^{-t} = 220-y\]
\[e^{-t} = \frac{(220-y)}{200}\]
\[-t = \ln\left(\frac{220-y}{200}\right)\]
\[-t = \ln(220-y) - \ln(200)\]
\[t = \ln(200)-\ln(220-y)\]
Replace all ys with t and t with W^-1(t)
\[W^{-1}(t) = \ln(220) - \ln(220-y)\]

Answer 4

Sorry, last line should be:
\[W^{-1}(t) = \ln(200) - \ln(220-t)\]