Chapter 5.2, Problem 17P

The amount $a$ you fill a tub varies directly with the amount of time $t$ you fill it. Suppose you fill 25 gallons in 5 minutes. What is an equation that relates $a$ and t ? What is the graph of the equation?

To determine

To determine the equation and the graph it.

Explanation of Solution

Given:

The amount a you fill a tub varies directly with the amount of time t you fill it.

25 gallons is filled in 5 minutes.

Calculation for graph:

When, $a=25$ gallons then, $t=5$ minutes

Thus,

  $\begin{array}{l}\Rightarrow \frac{a}{t}=\frac{25}{5}\\ \Rightarrow \frac{a}{t}=5\\ \Rightarrow a=5t\end{array}$

Hence, the required equation is $a=5t$ .

Graph:

  

Interpretation:

From the graph it can be observed that the horizontal extent of the graph is from $-\infty$ to $\infty$ .

And the vertical extent of the graph is also from $-\infty$ to $\infty$ .

So, both the domain and range of the function is $(-\infty ,\infty )$ .