Question

The student used the gift card to spend the same amount of money at the coffee shop every day until the remaining value of the card was $0. This function represents f(n), the value, in dollars, of the gift card after n days.f(n) = −2.5n + 75A. Based on the function, what was the original value, in dollars, of the giftcard? Show or explain how you got your answer.B. Based on the function, how much money, in dollars, did the student spend each day at the coffee shop? Show or explain how you got your answer.C. What was the remaining value, in dollars, of the gift card after 20 days? Show or explain how you got your answer.D. How many days in total did it take until the remaining value of the gift

Answer 1

A. The original value of the gift card is 75 dollars, which is the y-intercept of the function.

B. The student spent 2.5 dollars each day at the coffee shop, which is the coefficient of n in the function.

C. After 20 days, the remaining value of the gift card is -2.5 * 20 + 75 = 25 dollars.

D. To find the total number of days until the gift card was used up, we need to find when f(n) = 0. Setting the function equal to 0 and solving for n, we get: 0 = -2.5n + 75, so n = (75)/(-2.5) = 30 days.