Question

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

Answer 1

Answer:

$9\ years$

Step-by-step 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

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

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