What is the answer to B(t)=2190*e^{-0.3t} ?

The answer to B(t)=2190*e^{-0.3t} is t=(\W((657)/B))/(0.3)

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B(t)=2190*e^{-0.3t}

B (t) = 2190 \cdot e^{- 0.3 t}

t = \frac{W ( \frac{657}{B} )}{0.3}

Solution steps

B (t) = 2190 e^{- 0.3 t}

Prepare

B (t) = 2190 \cdot e^{- 0.3 t}

for Lambert form:

Bt e^{0.3 t} = 2190

Rewrite the equation with

0.3 t = u

and

t = \frac{u 10}{3}

B (\frac{u \cdot 10}{3}) e^{u} = 2190

Rewrite

B (\frac{u 10}{3}) e^{u} = 2190

in Lambert form:

e^{u} u = \frac{657}{B}

Solve

e^{u} u = \frac{657}{B} : u = W (\frac{657}{B})

u = W (\frac{657}{B})

Substitute back

u = 0.3 t,

solve for

t

Solve

0.3 t = W (\frac{657}{B}) : t = \frac{W ( \frac{657}{B} )}{0.3}

t = \frac{W ( \frac{657}{B} )}{0.3}

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What is the answer to B(t)=2190*e^{-0.3t} ?
The answer to B(t)=2190*e^{-0.3t} is t=(\W((657)/B))/(0.3)