Answer:
Approximately 1705 liters of oil leaked out during the first hour.
Step-by-step explanation:
We are given the following in the question:
The rate of oil leak is given by:
[tex]r(t) = 75 e^{-0.04}[/tex]
This function gives the rate of leakage in liters per minute.
We have to find the amount of water leak during the first hour.
It can be calculated as:
[tex]r(t) = 75 e^{-0.04t}\\\text{Integrating both sides}\\\\\displaystyle\int^{60}_0 = \int^{60}_0 75 e^{-0.04t}dt\\\\=\bigg[\dfrac{75 e^{-0.04t}}{-0.04}\bigg]^{60}_0\\\\=-1875\big[e^{-0.04(60)}-e^{0}\big]\\=-1875(0.0907-1)\\=1704.90\\\approx 1705[/tex]
Thus, approximately 1705 liters of oil leaked out during the first hour.
