Question

A shop has determined that the number of bottles of water they sell on a summer day is a function of the day’s high temperature, and is approximately given by () = 5 + 12, where is the day’s high temperature, and 80 ≤ ≤ 110. Suppose that the predicted high temperatures for the next 7 days are given in the table below.

Answer 1

Answer:

$\large\boxed{\large\boxed{T=t+94}}$

Explanation:

To find the expression of the high temperature of the day (T) as a function of the day (t), analyze the trend shown on the table.

The data in the column of the day (t) increases by 1, and the the data in the column of the high temperature increases by 1.

Thus, the slope is 1ºF per day.

The point-slope form of the equation of a  line is:

         $y-y_1=m(x-x_1)$

Where m is the slope and y₁, x₁ are the coordinates of any point on the line.

Using the point (2, 96) you get:

          $y-96=1(x-2)\\\\y-96=x-2\\\\y=x-2+96\\\\y=x+94$

Using the names T and t for y and x, respectively:

         $T=t+94$