Question:

Can someone please help me with this integration problem? ?

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An oil storage tank ruptures at time t=0 and oil leaks from the tank at a rate of r(t)liters per minute. How much oil (V) leaks out during the first hour? (Give answer to nearest liter.)

r(t)=85e^(-0.02t)

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  1. volume of oil leaks=definite integral[0,t]rdt=definite integral 85e^(-0.02t)dt=(85/(-.02))e^-.02t[0,t]=-...  at first hour, t=60minute..so volume of oil leaks=4250-4250e^-.02(60)=4250(1-.301)=4...


  2. The integral of 85e^(-0.02t) from t = 0 to t = 60 is 4250 - 4250e^(-1.2), which equals about 2969.92; rounding gives 2970 liters.

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