Question

The number of members in the band was 82 in 2000 and has decreased by 8% each year. Which model shows the band's membership in terms of t, the number of years since 2000?

Answer 1

Given:

The number of members in the band was 82 in 2000.

The number of members decreased by 8% each year.

Required:

We need to find the model for the given situation.

Explanation:

Let t be the number of years since 2000.

Let y be the number of members in t number of years since 2000.

The initial value is 82.

The number of members is decreasing.

Consider the exponential decay equation.

$y=82(1-\frac{8}{100})^t$$y=82(1-0.08)^t$$y=82(0.92)^t$

Final answer:

$y=82(0.92)^t$