What is the answer to (1100)/(1+99e^{-0.3t)}=275 ?

The answer to (1100)/(1+99e^{-0.3t)}=275 is t=(ln(33))/(0.3)

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(1100)/(1+99e^{-0.3t)}=275

\frac{1100}{1 + 99 e ^{- 0.3 t}} = 275

t = \frac{ln ( 33 )}{0.3}

Decimal Notation

t = 11.65502 \dots

Solution steps

\frac{1100}{1 + 99 e ^{- 0.3 t}} = 275

Multiply both sides by

1 + 99 e^{- 0.3 t}

\frac{1100}{1 + 99 e ^{- 0.3 t}} (1 + 99 e^{- 0.3 t}) = 275 (1 + 99 e^{- 0.3 t})

Simplify

1100 = 275 (1 + 99 e^{- 0.3 t})

Switch sides

275 (1 + 99 e^{- 0.3 t}) = 1100

Divide both sides by

275

1 + 99 e^{- 0.3 t} = 4

Move

1

to the right side

99 e^{- 0.3 t} = 3

Divide both sides by

99

e^{- 0.3 t} = \frac{1}{33}

Apply exponent rules

- 0.3 t = ln (\frac{1}{33})

Solve

- 0.3 t = ln (\frac{1}{33}) : t = \frac{ln ( 33 )}{0.3}

t = \frac{ln ( 33 )}{0.3}

Verify Solutions:

t = \frac{ln ( 33 )}{0.3}

True

The solution is

t = \frac{ln ( 33 )}{0.3}

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45 \cdot 1.18 6^{x} = x

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3^{2 x} - 36 (3^{x}) + 243 = 0

What is the answer to (1100)/(1+99e^{-0.3t)}=275 ?
The answer to (1100)/(1+99e^{-0.3t)}=275 is t=(ln(33))/(0.3)