What is the answer to 400=(500)/(1+4e^{0.5t)} ?

The answer to 400=(500)/(1+4e^{0.5t)} is t=-(4ln(2))/(0.5)

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400=(500)/(1+4e^{0.5t)}

400 = \frac{500}{1 + 4 e ^{0.5 t}}

t = - \frac{4 ln ( 2 )}{0.5}

Decimal Notation

t = - 5.54517 \dots

Solution steps

400 = \frac{500}{1 + 4 e ^{0.5 t}}

Multiply both sides by

1 + 4 e^{0.5 t}

400 (1 + 4 e^{0.5 t}) = \frac{500}{1 + 4 e ^{0.5 t}} (1 + 4 e^{0.5 t})

Simplify

400 (1 + 4 e^{0.5 t}) = 500

Divide both sides by

400

1 + 4 e^{0.5 t} = \frac{5}{4}

Move

1

to the right side

4 e^{0.5 t} = \frac{1}{4}

Divide both sides by

4

e^{0.5 t} = \frac{1}{16}

Apply exponent rules

0.5 t = ln (\frac{1}{16})

Solve

0.5 t = ln (\frac{1}{16}) : t = - \frac{4 ln ( 2 )}{0.5}

t = - \frac{4 ln ( 2 )}{0.5}

Verify Solutions:

t = - \frac{4 ln ( 2 )}{0.5}

True

The solution is

t = - \frac{4 ln ( 2 )}{0.5}

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1 6^{x - 9} = \frac{1}{2}

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e^{x + 8} = \frac{1}{e}

e^{4 x} = 4 e^{- x}

What is the answer to 400=(500)/(1+4e^{0.5t)} ?
The answer to 400=(500)/(1+4e^{0.5t)} is t=-(4ln(2))/(0.5)