Chapter 9.8, Problem 32PPE

To determine

To determine thefunction model that determines the number of customers at the second shop.

Answer to Problem 32PPE

The required equation is $y=\left(2.5\right)x+30$

Explanation of Solution

Given information:

Given modeled function for first shop is $y=0.25x^2-5x+80$

It is given that both the shops have the same number of customers on day 10 and 20.

Number of customers on day $10=0.25{\left(10\right)}^2-5\left(10\right)+80=55$

Number of customers on day $20=0.25{\left(20\right)}^2-5\left(20\right)+80=80$

Now let us take function $y=ax+b$ as the modeled function for number of customers of day.

Now according to question, we get,

  $\begin{array}{l}10a+b=55\\ 20a+b=80\end{array}$

Now we subtract both equations we get,

  $\begin{array}{l}10a+b-20a-b=25\\ 10a=25\\ a=2.5\end{array}$

Put $a=2.5$ in the derived equation we get $b=30$

Hence the required equation is $y=\left(2.5\right)x+30$