You head to the gym for a workout and get on a treadmill. You set a goal on the treadmill to burn 300 calories while running at a constant speed. The treadmill tells you how many total miles you have run, along with the number of calories you have left to burn. At one point during your workout, you look at the treadmill screen, and it tells you that after running 0.6 miles, you have 255 calories left to burn to meet your goal. Assume that there is a constant rate of change between the number of calories you burn and the number of miles you have been running. 2 points each

a. How many calories did you burn after running 0.6 miles?

b. How many calories will you burn after running 1 mile?

c. Define a linear function, c, that relates the number of miles you have run, x, to the number of calories you have left to burn, c(x).

d. How many calories do you have left to burn after running 1.5 miles?

e. How many miles do you have to run to meet your goal?

f. Does your function have a vertical intercept? If yes, what is it, and what does this vertical intercept represent in this context?