What is the inverse of P(t)=(100000)/(100+900e^{-t)} ?

The inverse of P(t)=(100000)/(100+900e^{-t)} is -ln((1000-t)/(9t))

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inverse of P(t)=(100000)/(100+900e^{-t)}

inverse

P (t) = \frac{100000}{100 + 900 e ^{- t}}

- ln (\frac{1000 - t}{9 t})

Solution steps

y = \frac{100000}{100 + 900 e ^{- t}}

Replace

t

with

y

t = \frac{100000}{100 + 900 e ^{- y}}

Solve for

y, t = \frac{100000}{100 + 900 e ^{- y}}

- ln (\frac{1000 - t}{9 t})

What is the inverse of P(t)=(100000)/(100+900e^{-t)} ?
The inverse of P(t)=(100000)/(100+900e^{-t)} is -ln((1000-t)/(9t))