Question

Select the function that meets the following criteria.

a. The function grows exponentially at a rate of 6%.
b. The function has a y-intercept of 100.

a) y = 100 * (1.06)^x
b) y = 100 * x^0.06
c) y = 100 * e^(0.06x)
d) y = 100 + 0.06x

Answer 1

The function that meets the given criteria is y = 100 * (1.06)^x. This function represents exponential growth at a rate of 6% with a y-intercept of 100.

Step-by-step explanation:

The function that meets the given criteria is y = 100 * (1.06)^x.

This function represents exponential growth at a rate of 6% since the base of the exponent is greater than 1. The initial value, or y-intercept, is 100.

For example, if we substitute x = 1 into the function, we get y = 100 * (1.06)^1 = 106. This means that after one unit of time, the value of y has grown to 106, which is a 6% increase from the initial value of 100.