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? if necessary, round your answer to the nearest whole number. tickets submit

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time in years.
Here, $P = 4307$, $r = 0.09$ (since 9% = 0.09), and $t = 9$.

Step2: Substitute the values into the formula

Substitute $P = 4307$, $r = 0.09$, and $t = 9$ into the formula:
$A = 4307(1 - 0.09)^9$
First, calculate $(1 - 0.09) = 0.91$.
Then, calculate $0.91^9$. Using a calculator, $0.91^9 \approx 0.424691477$.

Step3: Calculate the final amount

Multiply $4307$ by $0.424691477$:
$A = 4307 \times 0.424691477 \approx 1829.14$

Step4: Round to the nearest whole number

Rounding $1829.14$ to the nearest whole number gives $1829$.

Answer:

1829