What is the answer to t=20+70e^{-t} ?

The answer to t=20+70e^{-t} is t=\W_{0}((70)/(e^{20)})+20

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t=20+70e^{-t}

t = 20 + 70 e^{- t}

t = W_{0} (\frac{70}{e ^{20}}) + 20

Decimal Notation

t = 20.00000 \dots

Solution steps

t = 20 + 70 e^{- t}

Prepare

t = 20 + 70 e^{- t}

for Lambert form:

70 = (t - 20) e^{t}

Rewrite the equation with

t - 20 = u

and

t = u + 20

70 = ((u + 20) - 20) e^{(u + 20)}

Simplify

70 = e^{u + 20} u

Rewrite

70 = e^{u + 20} u

in Lambert form:

e^{u} u = \frac{70}{e ^{20}}

Solve

e^{u} u = \frac{70}{e ^{20}} : u = W_{0} (\frac{70}{e ^{20}})

u = W_{0} (\frac{70}{e ^{20}})

Substitute back

u = t - 20,

solve for

t

Solve

t - 20 = W_{0} (\frac{70}{e ^{20}}) : t = W_{0} (\frac{70}{e ^{20}}) + 20

t = W_{0} (\frac{70}{e ^{20}}) + 20

x, z = y^{3} e^{x^{2}}

5^{5 x - 2} = 40

10 e^{- 0.03 x} = 4

3 (2^{1 - x}) = 7^{x}

3^{x} + \frac{2}{3 ^{x - 1}} = 5

What is the answer to t=20+70e^{-t} ?
The answer to t=20+70e^{-t} is t=\W_{0}((70)/(e^{20)})+20