Question

And check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
Yolanda is filling her bathtub. The table shows the number of gallons of water in the
bathtub at different times since she started filling it.
Time
(minutes)
Water
(gallons)
16.50
1
1.5
24.75
2.
33
Answer the following questions based on the information in the table.
Part A
Find the constant of proportionality (in gallons per minute) using the values in the first
row of the table.

Answer 1

16.5 gallons per minute.

Explanation:

The given table is:

`\begin{center}\begin{tabular}{ c c } Time(minutes) & Water(gallons) \\ 1 & 16.50 \\ 1.5 & 24.75 \\ 2 & 33 \\\end{tabular}\end{center}`

We are given this linear function in the form of table.

Let 't' be the time and W(t) be the function with which the gallons of water are changing with time.

We can use slope intercept form to find the equation.

`y=mx+c`

Slope of a function:

`m=(y_2-y_1)/(x_2-x_1)`

`x_2 = 1.5\\x_1 = 1\\y_2 = 24.75\\y_1 = 16.50`

`m=(24.75-16.50)/(1.5-1)\\\Rightarrow m =16.5`

This slope is the constant of proportionality.

i.e. the rate at which the number of gallons are changing per minute.

So, the answer is 16.5 gallons per minute.