Question

What type of exponential function is f(x) = 0.75 * 0.1^x, and what is the function's percent rate of change?

A) Exponential decay
B) Exponential growth
C) Exponential constant
D) Exponential inverse

Answer 1

The function f(x) = 0.75 * 0.1^x represents exponential decay with a percent rate of change of 90% decay per unit increase in x.

Step-by-step explanation:

The function described is f(x) = 0.75 \* 0.1^x. To determine whether it represents exponential growth or decay, we look at the base of the exponent, which is 0.1. Since 0.1 is less than 1, the function is an example of exponential decay, not growth, constant, or inverse.

To find the function's percent rate of change, we identify the base of the exponent (0.1 in this case) and translate it into a percent change. We can express 0.1 as 10%, meaning the quantity decreases by 90% each time x increases by 1.

The percent rate of change of the function is 90% decay per unit increase in x.