Question

The Winchester Opera House sold 4,600 tickets this year, but it has been experiencing a 10%drop in sales from one year to the next. If this trend continues, then how many tickets willthe opera house sell 8 years from now?

Answer 1

Exponential decay formula:

`y=a(1-r)^t`

y is the number of tickets sold at t years

a is the initial number of tickets sold

r is the rate of drop (in decimal form)

t is the time in years

`y=4600(1-0.1)^t`

8 years from now:

`\begin{gathered} y=4600(1-0.1)^8 \\ \\ y=4600(0.9)^8 \\ \\ y=1980.149 \end{gathered}`

Then, if the trend continues, 8 years from now the number of tickets sell will be approximately 1980