What is the inverse of f(x)=5000e^{-0.0005x} ?

The inverse of f(x)=5000e^{-0.0005x} is -(ln(x/(5000)))/(0.0005)

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inverse of f(x)=5000e^{-0.0005x}

inverse

f (x) = 5000 e^{- 0.0005 x}

- \frac{ln ( \frac{x}{5000} )}{0.0005}

Solution steps

y = 5000 e^{- 0.0005 x}

Replace

x

with

y

x = 5000 e^{- 0.0005 y}

Solve for

y, x = 5000 e^{- 0.0005 y}

- \frac{ln ( \frac{x}{5000} )}{0.0005}

f (x) = ln (2 - x) - 1

f (x) = 7 + 3 x - 6

f (x) = 3 x - 2

6 + 3 + x

f (x) = 12 - 2 x + \frac{5}{2}

What is the inverse of f(x)=5000e^{-0.0005x} ?
The inverse of f(x)=5000e^{-0.0005x} is -(ln(x/(5000)))/(0.0005)