Question

Given the following exponential function, identify whether the change
represents growth or decay, and determine the percentage rate of increase or
decrease.
y = 38(1.09)^x

Answer 1

Step-by-step explanation:

We can determine whether the change represents exponential growth or exponential decay by making a table for a few values of x.

0 -> $38(1.09)^0$ = 38 * 1 = 38

1 -> $38(1.09)^1$= 38 * 1.09 = 41.42

2 -> 38(1.09)² = 38 * 1.09 * 1.09 = 45.1478

We see that y increases as x increases, which makes this function represent exponential growth.

The percentage rate of increase is how much the value of y increases by each time x increases.

Since we are multiplying by 1.09 each time, we are taking 109% of the previous y value to get the current y value. Hence, the rate of increase is 9%.