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.