Question

Determine the exponential function with an initial value of 5, increasing at a rate of 17% per year.

a) 5 * 0.983ˣ
b) 5 * 1.17ˣ
c) 5 * 0.83ˣ
d) 5 * 1.017ˣ

Answer 1

The correct exponential function representing an initial value of 5 and an annual growth rate of 17% is b) 5 * 1.17ˣ.

Step-by-step explanation:

The question asks to determine the exponential function that represents a quantity with an initial value of 5, increasing at an annual rate of 17%. An exponential function is generally written in the form f(x) = a * bˣ, where a is the initial value and b is the base representing the growth factor.

Given an initial value a = 5 and an annual growth rate of 17%, the growth factor b can be determined by adding 100% of the initial amount to the 17% increase, which gives us b = 1 + 0.17 = 1.17. Therefore, the exponential function that represents the scenario described is f(x) = 5 * 1.17ˣ, which corresponds to option b) 5 * 1.17ˣ.