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#