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

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.