The number of subscribers, f(t), to a magazine after t years is shown by the equation below:

Question

f(t) = 95(0.75)t

Which conclusion is correct about the number of subscribers to the magazine?

It increased by 25% every year.
It decreased by 25% every year.
It increased by 75% every year.
It decreased by 75% every year.

Answer 1

To analyze the function \( f(t) = 95(0.75)^t \), we need to focus on the base of the exponential term, which is \( 0.75 \).

The base \( 0.75 \) indicates that the number of subscribers is multiplied by \( 0.75 \) each year. This means the subscribers are dropping to 75% of the previous year's amount. Consequently, the magazine is experiencing a decrease in subscribers.

To quantify this decrease, we can calculate the percentage decrease:

1. From 100%, if it goes to 75%, it decreases by \( 100% - 75% = 25% \).

Therefore, we conclude that:

It decreased by 25% every year.