A: write the equation of the exponential function that models the average price of a movie ticket t years after 2010.

after 1 year the ticket will be: 10 + 0.05*10 =10(1 + 0.05)

after 2 years the ticket will be: 10(1 + 0.05) + 10(1 + 0.05)*0.05 = 10(1 + 0.05)^2

after 3 years the ticket will be: 10(1 + 0.05)^3

after x years the ticket will be

f(x) = 10(1 + 0.05)^x, where x is the number of years after 2010

B: use the model to predict the average price of a movie ticket in 2015

for the year 2015, x = 2015 - 2010 = 5

f(5) = 10(1 + 0.05)^5

f(5) = $12.73

the average price of a movie ticket in 2015 will be $12.73.