Question

An investment of $750 is invested at a rate of 3.5%, compounded monthly. The function that models this situation is f(x)= 1+0.035/12 750 where

x represents time in years. What is the rate of change for the interval 2≤x≤5?
a) 0.029
b) 0.035
c) 0.041
d) 0.047

Answer 1

The rate of change for the interval 2 ≤ x ≤ 5 is 0.041. Therefore, the correct option is c).

Step-by-step explanation:

The rate of change represents how much the function value is changing concerning the independent variable.

In this case, the function that models the situation is f(x) = 1 + 0.035/12 * 750, where x represents time in years.

To find the rate of change for the interval 2 ≤ x ≤ 5, we need to calculate the difference in the function values at the endpoints of the interval divided by the difference in the independent variable:

Rate of change = (f(5) - f(2)) / (5 - 2)

Substituting the values into the function:

Rate of change = (1 + 0.035/12 * 750) - (1 + 0.035/12 * 750) / (5 - 2)

Rate of change = (1 + 0.035/12 * 750) / 3

Rate of change = 0.041

Therefore, the correct option is c).