Question

Given the exponential model y= 200(.80)^x, tell whether the model represents exponential growth or decay. Then, tell what the growth/decay factor is and the growth/decay percent.

Answer 1

The given exponential model y = 200(.80)^x represents exponential decay with a decay factor of 0.80 and a decay percent of -20%.

Step-by-step explanation:

The given exponential model is y = 200(.80)^x.

To determine whether the model represents exponential growth or decay, we need to examine the base of the exponential function, which is 0.80 in this case.

If the base is greater than 1, the model represents exponential growth. If the base is between 0 and 1, the model represents exponential decay.

In this case, the base 0.80 is between 0 and 1, so the model represents exponential decay.

The growth/decay factor is the value of the base, which is 0.80. The growth/decay percent is equal to 100 times the base minus 100.

Therefore, the growth/decay factor is 0.80 and the growth/decay percent is -20%.

Answer 2

This function represents exponential decay.

We know it's exponential because the value the base (200) is being multiplied by is being raised to the power of x.

In this case, the multiplication value is 0.8, which is less than 1.

If the multiplication value is less than 1, than the function will decay, rather than grow.

In this case, the factor is 0.8, or 80%.