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

Explanation:

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).

Answer 2

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).