How much oil leaks from the tank in the first four hours?

Question

Oil is leaking from a storage facility at the rate $L(t)=400e^(-.2t)$ gallons per hour where t is the time in hours. How much oil leaks from the tank in the first four hours?

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Answer 1 · 2018-05-29T08:43:56

$1101.342$ gallons

To find the amount of oil leaked in the first $4$ hours, write a definite integral to express the amount of oil leaked in $4$ hours.

$int_0^4L(t)color(white)(.)dt$

Simplify,

$int_0^4 400e^(-0.2t)color(white)(.)dt$

Move the constant out,

$400int_0^4 e^(-0.2t)color(white)(.)dt$

Integrate,

$400[-5e^(-0.2t)]_0^4$

Apply limits,

$400[(-5e^-0.8)-(-5)]$

Expand,

$2000-2000e^-0.8$

Evaluate,

$1101.342$