Question

Oil is leaking from a tanker at the rate of R(t)=2,000e^(-0.2t) gallons per hour, where t is measured in hours. How much oild has leaked out of the tanker after 10 hours?

Answer 1

amount of oil = Rate * time

since rate is continuously changing we have to use "dt" for time and integrate to get this solution
\[\rightarrow \int\limits_0^{10} R(t) dt\]
\[2000 \int\limits_0^{10} e^{-.2t} dt = 2000 |_0^{10} \frac{e^{-.2t}}{-.2} = 2000(\frac{e^{-2} - 1}{-.2})\]