Question

tristan uses a cistern to fill a tub with water. when he begins, at time ( t = 0 ) minutes, the tub is empty and there are 5812 l of water in the cistern. at time ( t = 15 ) minutes, the cistern contains 5490 l of water and the tub contains 322 l of water. find the average rate of change in the amount of water in the cistern from ( t = 0 ) to ( t = 15 ) minutes, rounding your answer to three decimal places, with appropriate units. then fill in the guided sentence below to interpret the meaning of your answer in context.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Let \(y\) be the amount of water in the cistern and \(t\) be the time. Here, \(x_1=0\), \(f(x_1) = 5812\), \(x_2 = 15\), and \(f(x_2)=5490\).

Step2: Substitute the values into the formula

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Answer:

The average rate of change in the amount of water in the cistern from \(t = 0\) to \(t=15\) minutes is \(-21.467\) liters per minute. This means that, on average, the amount of water in the cistern is decreasing at a rate of approximately \(21.467\) liters per minute over the 15 - minute time interval.