Question

An investor deposited $5000 in an account that earns 1% annual interest. The amount of money in the account is represented by the function f(x) = 5000(1.01)x, where x represents the number of years since the account was opened. What is the average rate of change of the function between x=2 and x=7? Round to the nearest cent (two decimal places).

Answer 1

The average rate of change of the function f(x) = 5000(1.01)^x between x=2 and x=7 is 50.41.

Step-by-step explanation:

The average rate of change of a function can be found by calculating the difference in the function values at the two given points and dividing by the difference in the input values. In this case, we are given the function f(x) = 5000(1.01)^x and asked to find the average rate of change between x=2 and x=7.

To find the difference in function values, we evaluate the function at each point: f(2) = 5000(1.01)^2 = 5105 and f(7) = 5000(1.01)^7 = 5357.07. The difference in function values is: 5357.07 - 5105 = 252.07.

The difference in input values is: 7 - 2 = 5. Now, we can calculate the average rate of change as: 252.07 / 5 = 50.41.