Question

a burrito company uses the function $c(x) = 1.74x^2$ to calculate the number of calories in a tortilla with a diameter of $x$ inches.
a. find the average rate of change of the function over the intervals $6 < x < 8$ and $9 < x < 11$.
b. interpret the average rates of change.
c. what does the difference in the average rates of change mean in terms of the situation?

a. the average rate of change of $c(x)$ over $6 < x < 8$ is $24.36$.
(simplify your answer. type an integer or a decimal.)

the average rate of change of $c(x)$ over $9 < x < 11$ is $square$.
(simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \( C(x) \) over the interval \( a < x < b \) is given by \( \frac{C(b) - C(a)}{b - a} \).

Step2: Identify \( a \), \( b \) for the interval \( 9 < x < 11 \)

Here, \( a = 9 \) and \( b = 11 \). The function is \( C(x)=1.74x^{2} \).

Step3: Calculate \( C(11) \) and \( C(9) \)

First, calculate \( C(11) \):
\( C(11)=1.74\times(11)^{2}=1.74\times121 = 210.54 \)
Then, calculate \( C(9) \):
\( C(9)=1.74\times(9)^{2}=1.74\times81 = 140.94 \)

Step4: Apply the average rate of change formula

Using the formula \( \frac{C(11)-C(9)}{11 - 9} \), substitute the values:
\( \frac{210.54 - 140.94}{2}=\frac{69.6}{2}=34.8 \)

Answer:

34.8