Question

Oil is leaking from a tanker at the rate of R(t) = 2000e^(-0.2t) gallons per hour where t is measured in hours. How much oil leaks out of the tanker from the time t = 0 to t = 10
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Answer 1

We first integrate the expression to find the oil leaked since we have an expression for leakage rate.
Integrating:
O(t) = -10000exp(-0.2t); substituting t = 10
O(t) = -1,353 gallons
1,353 gallons of oil leak out in the first 10 seconds.