Question

The annual inflation rate is 3.5% per year. If a movie costs $7.50, determine which of the following graphs best models the change in price, with respect to time, of the movie ticket.

Answer 1

Let's model the cost by the following exponential function:
 c (t) = (7.50) * (1.035) ^ t
 Where,
 c (t): cost of the movie after t years.
 7.50: initial cost of the movie in $
 1,035: annual percentage increase due to inflation.
 t: time in years.
 for t = 0 We have:
 c (t) = (7.50) * (1.035) ^ 0
 c (t) = (7.50) * (1)
 c (t) = 7.50
 Answer:
 The graph that best models the function is:
 GRAPH 2 (from left to right).