Chapter 1.5, Problem 83E

a.

To determine

To find:the function that represents the total annual sales of the two stores.

Answer to Problem 83E

The function that represents the total annual sales of the two stores is $T=1322+1.3t^2+72.4t$.

Explanation of Solution

Given information :

The functions are $S_1=973+1.3t^2$ and $S_2=349+72.4t$

Calculation :

To find the function that represents the total annual sales of the two stores, add their annual sales,

  $\begin{array}{l}T=S_1+S_2\\ T=973+1.3t^2+349+72.4t\text{ [}{S}_1=973+1.3t^2,S_2=349+72.4t]\\ T=\left(973+1.3t^2\right)+\left(349+72.4t\right)\\ T=1322+1.3t^2+72.4t\text{ [add]}\end{array}$

Thus, the function that represents the total annual sales of the two stores is $T=1322+1.3t^2+72.4t$.

b.

To determine

To graph: the functions by using graphing utility.

Explanation of Solution

Given information :

The functions are $S_1=973+1.3t^2$ , $S_2=349+72.4t$ , $T=1322+1.3t^2+72.4t$.

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression which is required to graph,

  $973+1.3t^2$ , $349+72.4t$ , $1322+1.3t^2+72.4t$

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  

Interpretation: from the above graph it can be observed that the $T$ represent the total annual amount of two stores.