Question

A function is shown.

f(x) = 50,900(1.03)x
To the nearest whole number, what is the average rate of change of the function over the interval from x = 0 to x = 15?
A.1,775
B.1,893
C.2,028
D.2,184

Answer 1

The average rate of change of the function f(x) = 50,900(1.03)^x over the interval from x = 0 to x = 15 is calculated to be approximately 1,893.85, which rounds to 1,894 to the nearest whole number.

Step-by-step explanation:

To calculate the average rate of change of the function f(x) = 50,900(1.03)x over the interval from x = 0 to x = 15, you can use the following formula:

Average rate of change = \( \frac{{f(15) - f(0)}}{{15 - 0}} \)

First, calculate the values of f(x) at the endpoints of the interval:

• f(0) = 50,900(1.03)0 = 50,900
• f(15) = 50,900(1.03)15

Next, evaluate f(15) and then calculate the average rate of change:

• f(15) = 50,900(1.03)15 ≈ 50,900 \( \times \) 1.558853626 = 79,307.74531
• Average rate of change = \( \frac{{79,307.74531 - 50,900}}{{15}} \) ≈ 1,893.85

Therefore, to the nearest whole number, the average rate of change of the function over the interval from x = 0 to x = 15 is 1,894.