What is the inverse of (20)/(1+e^{-0.3*(t-15))} ?

The inverse of (20)/(1+e^{-0.3*(t-15))} is -(ln((20)/t-1))/(0.3)+15

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inverse of (20)/(1+e^{-0.3*(t-15))}

inverse

\frac{20}{1 + e ^{- 0.3 \cdot (t - 15)}}

- \frac{ln ( \frac{20}{t} - 1 )}{0.3} + 15

Solution steps

y = \frac{20}{1 + e ^{- 0.3 (t - 15)}}

Replace

t

with

y

t = \frac{20}{1 + e ^{- 0.3 (y - 15)}}

Solve for

y, t = \frac{20}{1 + e ^{- 0.3 \cdot (y - 15)}}

- \frac{ln ( \frac{20}{t} - 1 )}{0.3} + 15

f (x) = 2 (\frac{x - 5}{2}) + 5

\frac{3 x - 4}{5 x + 6}

f (x) = 0.005 x^{3}

f (x) = arctan (\frac{1}{3})

f (x) = \frac{1}{2} x^{2} - 4 x + \frac{39}{8}

What is the inverse of (20)/(1+e^{-0.3*(t-15))} ?
The inverse of (20)/(1+e^{-0.3*(t-15))} is -(ln((20)/t-1))/(0.3)+15