Question

question jace uses a cistern to fill a tub with water. when he begins, at time t = 0 minutes, the tub is empty and there are 6387 l of water in the cistern. at time t = 21 minutes, the cistern contains 6262 l of water and the tub contains 125 l of water. find the average rate of change in the amount of water in the tub from t = 0 to t = 21 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. answer the average rate of change is. it represents that the is at a rate of over that time interval.

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, the amount of water in the tub is the function of time $t$. At $t_1 = 0$, the amount of water in the tub $y_1=0$ L, and at $t_2 = 21$ minutes, the amount of water in the tub $y_2 = 125$ L.

Step2: Calculate the average rate of change

Using the formula $\frac{y_2 - y_1}{t_2 - t_1}$, we substitute $y_1 = 0$, $y_2=125$, $t_1 = 0$, and $t_2 = 21$. So, $\frac{125-0}{21 - 0}=\frac{125}{21}\approx5.952$ L/min.

Answer:

The average rate of change is $5.952$ L/min. It represents that the amount of water in the tub is increasing at a rate of $5.952$ liters per minute over that time interval.