Colton was given a box of assorted chocolates for his birthday. Each night, Colton treated himself to some chocolates. There were originally 30 chocolates in the box and Colton ate 2 chocolates each night. Write an equation for C, C, in terms of t, t, representing the number of chocolates remaining in the box tt days after Colton's birthday.

Given:

Initial number of chocolates in the box = 30

Colton ate 2 chocolates each night.

To find:

The equation for the number of chocolates remaining in the box t days after Colton's birthday.

Solution:

Let C be the chocolates remaining in the box and t is number of days after Colton's birthday.

Colton ate 2 chocolates each night. It means, the remaining number of chocolates decreased by 2 per day.

Initial number of chocolates in the box is 30 and it decreased by 2 per day. So, the equation for remaining chocolates is

Therefore, the required equation is .

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.