What is the answer to (1000)/(4+6e^{-t)}=200 ?

The answer to (1000)/(4+6e^{-t)}=200 is t=ln(6)

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(1000)/(4+6e^{-t)}=200

\frac{1000}{4 + 6 e ^{- t}} = 200

t = ln (6)

Decimal Notation

t = 1.79175 \dots

Solution steps

\frac{1000}{4 + 6 e ^{- t}} = 200

Multiply both sides by

4 + 6 e^{- t}

\frac{1000}{4 + 6 e ^{- t}} (4 + 6 e^{- t}) = 200 (4 + 6 e^{- t})

Simplify

1000 = 200 (4 + 6 e^{- t})

Switch sides

200 (4 + 6 e^{- t}) = 1000

Divide both sides by

200

4 + 6 e^{- t} = 5

Move

4

to the right side

6 e^{- t} = 1

Divide both sides by

6

e^{- t} = \frac{1}{6}

Apply exponent rules

- t = ln (\frac{1}{6})

Solve

- t = ln (\frac{1}{6}) : t = ln (6)

t = ln (6)

Verify Solutions:

t = ln (6)

True

The solution is

t = ln (6)

3^{x + 2} = 5^{x}

2^{x - 2} = 4

lo g_{10} (2^{x}) = \frac{3}{2}

5^{x^{2}} = 2 5^{x}

2^{x} = \frac{4 ^{7}}{8 ^{3}}

What is the answer to (1000)/(4+6e^{-t)}=200 ?
The answer to (1000)/(4+6e^{-t)}=200 is t=ln(6)