Question

The Oakdale Opera House sold 4,307 tickets this year, but it has been experiencing a 9% drop in sales from one year to the next. If this trend continues, then how many tickets will the opera house sell 9 years from now?

Answer 1

To find the number of tickets the Oakdale Opera House will sell in 9 years' time, considering a 9% annual drop in sales, we apply the exponential decay formula to the initial ticket sales of 4,307.

Step-by-step explanation:

The Oakdale Opera House is experiencing a 9% drop in ticket sales each year. To calculate how many tickets it will sell 9 years from now, we will use the formula for exponential decay, which is:

Final amount = Initial amount × (1 - rate of decay)number of periods

In this case, the initial amount of tickets sold is 4,307, the rate of decay is 9%, or 0.09, and the number of periods is 9 years. Therefore, the calculation would be:

Tickets in 9 years = 4,307 × (1 - 0.09)9

Calculating the above will give us the number of tickets sold after 9 years considering the continuous 9% annual decline.