the function $h(x)=-x^{2}+4x - 1$ represents the amount of water in a tank (in liters) at hour $x$…

the function $h(x)=-x^{2}+4x - 1$ represents the amount of water in a tank (in liters) at hour $x$. determine the average rate of change of the amount of water over the interval $1leq xleq4$ and interpret the result. use the drop - down arrows to complete the sentences. the average rate of change of the amount of water in the tank over the interval $1leq xleq4$ is. this means that, on average, the amount of water in the tank

the function $h(x)=-x^{2}+4x - 1$ represents the amount of water in a tank (in liters) at hour $x$. determine the average rate of change of the amount of water over the interval $1leq xleq4$ and interpret the result. use the drop - down arrows to complete the sentences. the average rate of change of the amount of water in the tank over the interval $1leq xleq4$ is. this means that, on average, the amount of water in the tank

Answer

Answer:

-1

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 1$, $b = 4$, and $h(x)=-x^{2}+4x - 1$.

Step2: Calculate $h(4)$

$h(4)=-(4)^{2}+4\times4 - 1=-16 + 16-1=-1$.

Step3: Calculate $h(1)$

$h(1)=-(1)^{2}+4\times1 - 1=-1 + 4-1=2$.

Step4: Calculate average rate of change

$\frac{h(4)-h(1)}{4 - 1}=\frac{-1-2}{3}=\frac{-3}{3}=-1$.

This means that, on average, the amount of water in the tank decreases by 1 liter per hour.