Question

Determine if the function is a growth or decay and the percent of increase and decrease

y = 5(.25)x




y = 5(.5)x



y = 4(1.018)x



y = 12 (1 - .08

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the function is a growth or decay, we need to look at the base of the exponential term.

1) For the function y = 5(.25)x:
The base of the exponential term is 0.25, which is less than 1. Therefore, this function represents exponential decay.

2) For the function y = 5(.5)x:
The base of the exponential term is 0.5, which is less than 1. Therefore, this function also represents exponential decay.

3) For the function y = 4(1.018)x:
The base of the exponential term is 1.018, which is greater than 1. Therefore, this function represents exponential growth.

4) For the function y = 12 (1 - .08):
This function does not have an exponential term, so it does not represent exponential growth or decay.

Now, let's calculate the percent increase or decrease for the functions that represent growth or decay.

1) For the function y = 5(.25)x:
Since this function represents exponential decay, the percent decrease can be calculated using the formula (1 - base) * 100.
Percent decrease = (1 - 0.25) * 100 = 0.75 * 100 = 75%

2) For the function y = 5(.5)x:
Since this function also represents exponential decay, the percent decrease can be calculated using the formula (1 - base) * 100.
Percent decrease = (1 - 0.5) * 100 = 0.5 * 100 = 50%

3) For the function y = 4(1.018)x:
Since this function represents exponential growth, the percent increase can be calculated using the formula (base - 1) * 100.
Percent increase = (1.018 - 1) * 100 = 0.018 * 100 = 1.8%

The function y = 12 (1 - 0.08) does not involve exponential growth or decay, so there is no percent increase or decrease to calculate.