Question

An oil storage tank ruptures at time t = 0 t=0 and oil leaks from the tank at a rate of r ( t ) = 75 e − 0.04 t(t)=75e-0.04to liters per minute. How much oil leaks out during the first hour

Answer 1

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:

$r(t) = 75 e^{-0.04}$

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:

$r(t) = 75 e^{-0.04t}\\\text{Integrating both sides}\\\\\displaystyle\int^{60}_0 = \int^{60}_0 75 e^{-0.04t}dt\\\\=\bigg[\dfrac{75 e^{-0.04t}}{-0.04}\bigg]^{60}_0\\\\=-1875\big[e^{-0.04(60)}-e^{0}\big]\\=-1875(0.0907-1)\\=1704.90\\\approx 1705$

Thus, approximately 1705 liters of oil leaked out during the first hour.