Question

If the price of theater tickets increases at 8% per year, about how long will it take to double the price?

Answer 1

`9\ years`

Explanation:

Let

P----> the initial price of the ticket

y ---> the price of the ticket after t years

t---> the time in years

we know that

100%+8%=108%=108/100=1.08

so

`y=P(1.08)^(t)` ----> equation A

If the price is doubled

then

`y=2P` -----> equation B

equate equation A and equation B and solve for t

`2P=P(1.08)^(t)`

Simplify

`2=(1.08)^(t)`

Apply log both sides

`log(2)=t*log(1.08)`

`t=log(2)/log(1.08)=9\ years`