Question

question a new budgeting app was launched three years ago. in the apps 6th quarter, sales stood at 139 thousand dollars, while in the 11th quarter, sales stood at 237.95 thousand dollars. find the average rate of change from t = 6 to t = 11 quarters, 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 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, $a = 6$, $b = 11$, $f(6)=139$ (in thousands of dollars) and $f(11)=237.95$ (in thousands of dollars).

Step2: Substitute values into the formula

$\frac{f(11)-f(6)}{11 - 6}=\frac{237.95 - 139}{11 - 6}=\frac{98.95}{5}$

Step3: Calculate the result

$\frac{98.95}{5}=19.790$

Answer:

The average rate of change is $19.790$ thousand dollars per quarter. It represents that the sales is increasing at a rate of $19.790$ thousand dollars per quarter over that time interval.