Question

question an engineer collects data on power (in kilowatts) generated by a wind turbine over time. at time t = 8 months, the turbine’s production is 3 kw, and at time t = 12 months, the turbine’s production is 31 kw. find the average rate of change from t = 8 to t = 12 months, 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 $y = f(t)$ from $t = a$ to $t = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 8$, $f(a)=3$, $b = 12$, and $f(b)=31$.

Step2: Substitute values into formula

$\frac{f(12)-f(8)}{12 - 8}=\frac{31 - 3}{12 - 8}=\frac{28}{4}=7.000$

Answer:

The average rate of change is $7.000$ kW per month. It represents that the power generated by the wind - turbine is increasing at a rate of $7.000$ kW per month over that time interval.