Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y=540(1.04)^x

Answer 1

The function y=540(1.04)^x represents exponential growth. The rate of increase can be determined by finding the value of 1.04^x.

For example, if x=1, then the value of 1.04^1 is 1.04, which represents a 4% increase. If x=2, then the value of 1.04^2 is 1.0816, which represents an 8.16% increase. If x=3, then the value of 1.04^3 is 1.1265, which represents a 12.65% increase.

In general, as the value of x increases, the value of 1.04^x increases at a faster rate, resulting in an exponential growth curve. The percentage rate of increase is determined by the value of 1.04. In this case, the percentage rate of increase is 4% per unit increase in x.