What is the answer to 5=(80)/(8+12e^{-0.6t)} ?

The answer to 5=(80)/(8+12e^{-0.6t)} is t=-(ln(2/3))/(0.6)

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5=(80)/(8+12e^{-0.6t)}

5 = \frac{80}{8 + 12 e ^{- 0.6 t}}

t = - \frac{ln ( \frac{2}{3} )}{0.6}

Decimal Notation

t = 0.67577 \dots

Solution steps

5 = \frac{80}{8 + 12 e ^{- 0.6 t}}

Multiply both sides by

8 + 12 e^{- 0.6 t}

5 (8 + 12 e^{- 0.6 t}) = \frac{80}{8 + 12 e ^{- 0.6 t}} (8 + 12 e^{- 0.6 t})

Simplify

5 (8 + 12 e^{- 0.6 t}) = 80

Divide both sides by

5

8 + 12 e^{- 0.6 t} = 16

Move

8

to the right side

12 e^{- 0.6 t} = 8

Divide both sides by

12

e^{- 0.6 t} = \frac{2}{3}

Apply exponent rules

- 0.6 t = ln (\frac{2}{3})

Solve

- 0.6 t = ln (\frac{2}{3}) : t = - \frac{ln ( \frac{2}{3} )}{0.6}

t = - \frac{ln ( \frac{2}{3} )}{0.6}

Verify Solutions:

t = - \frac{ln ( \frac{2}{3} )}{0.6}

True

The solution is

t = - \frac{ln ( \frac{2}{3} )}{0.6}

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What is the answer to 5=(80)/(8+12e^{-0.6t)} ?
The answer to 5=(80)/(8+12e^{-0.6t)} is t=-(ln(2/3))/(0.6)