Solve 80=250*e^(-15t)

Evaluate

80 = 250 e^{- 15 t}

Swap the sides of the equation

250 e^{- 15 t} = 80

Divide both sides

\frac{250 e ^{- 15 t}}{250} = \frac{80}{250}

Divide the numbers

e^{- 15 t} = \frac{80}{250}

Cancel out the common factor 10

e^{- 15 t} = \frac{8}{25}

Take the logarithm of both sides

ln (e^{- 15 t}) = ln (\frac{8}{25})

Evaluate the logarithm

- 15 t = ln (\frac{8}{25})

Change the signs on both sides of the equation

15 t = - ln (\frac{8}{25})

Divide both sides

\frac{15 t}{15} = \frac{- ln ( \frac{8}{25} )}{15}

Divide the numbers

t = \frac{- ln ( \frac{8}{25} )}{15}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

t = - \frac{ln ( \frac{8}{25} )}{15}

Solution

More Steps

t = \frac{- 3 ln ( 2 ) + 2 ln ( 5 )}{15}

Alternative Form

t \approx 0.075962

Solve the equation