Question

In 2012, the cost of a hamburger at a famous nationwide restaurant chain was $4.32. In 2022 the

price of the same hamburger is $6.12.

a. What is the average rate of change in the cost of the hamburger during this period?

b. Using the price in 2012 as an initial value, write a linear equation that models the cost of
the hamburger.

c. Using the model from part b, when will the price of the hamburger reach $7.02?

Answer 1

Explanation:

a. The average rate of change in the cost of the hamburger during the period from 2012 to 2022 can be calculated as the difference in the cost of the hamburger divided by the number of years between the two prices.

So, the average rate of change in the cost of the hamburger is:

(6.12 - 4.32) / (2022 - 2012) = 0.18

Therefore, the average rate of change in the cost of the hamburger during this period is $0.18 per year.

b. We can use the point-slope form of a linear equation to model the cost of the hamburger as it changes over time. Let y be the cost of the hamburger in dollars, and t be the number of years since 2012. We know that the cost of the hamburger in 2012 was $4.32, so we have a starting point of (0, 4.32).

Using the average rate of change calculated in part a, we can find the slope of the line:

slope = (6.12 - 4.32) / (2022 - 2012) = 0.18

Now we can write the equation of the line as:

y - 4.32 = 0.18t

y = 0.18t + 4.32

So, the linear equation that models the cost of the hamburger in terms of years since 2012 is y = 0.18t + 4.32.

c. To find when the cost of the hamburger will reach $7.02, we can substitute y = 7.02 into the equation we found in part b and solve for t:

7.02 = 0.18t + 4.32

2.7 = 0.18t

t = 15

So, the cost of the hamburger will reach $7.02 in the year 2012 + 15 = 2027.