Question

A pancake company uses the

function f(x) = 1.5x² to calculate
the number of calories in a
pancake with a diameter of x cm.
What is the average rate of change
for the function over the interval
10 A.) 150 calories per cm of diameter
B.) 33 calories per cm of diameter
C.) 65calories per cm of diameter
D.) 215 calories per cm of diameter

Answer 1

To find the average rate of change of the function f(x) = 1.5x² over the interval [10, 11], we need to calculate the change in f(x) over the interval, and divide by the change in x.

The change in f(x) over the interval [10, 11] is:

f(11) - f(10) = (1.511^2) - (1.510^2) = 165 - 150 = 15

The change in x over the interval [10, 11] is:

11 - 10 = 1

Therefore, the average rate of change of the function over the interval [10, 11] is:

(15/1) = 15

This means that for every 1 cm increase in diameter (i.e., for every 1 unit increase in x), the number of calories in the pancake increases by an average of 15 calories per cm of diameter.

Therefore, the answer is (A) 150 calories per cm of diameter.