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.
a) Express the high temperature as a function of High temperature, (degrees F)

Answer 1

Answer:

•          $T=t+94$

                 Where T is the hight temperature and t is the day

Explanation:

The table shows that every day the High temperature, T (degrees F) increases 1 unit.

Then, this is a linear function with slope = 1ºF / day.

You can use the point-slope equation to determine the function of the high temperature:

• Point-slope equation:

       $y-y_1=m(x-x_1)$

• Choose any point from the table and m = 1. I will use the first point (1,95)

• m = 1

• x₁ = 1

• y₁ = 95

Substitute:

        $y-95=1(x-1)\\\\y=x-1+95\\\\y=x+94$

Make the variables  y = T, and x = t:

     $T=t+94$