Chapter 7.4, Problem 97STP

To determine

To find: The reasonable domain and range for the given function.

Answer to Problem 97STP

The domain of $b$ is $D:\left\{b|0\le b\le 8\right\}$ and the range of $A$ for the given function is $R:\left\{A|0\le A\le 9600\right\}$ .

Explanation of Solution

Given information: For a function, $b$ represents the number of bags is $A\left(b\right)=1200b$ and the number of bags are $8$ . The area covered by each bag is $1200{\text{ft}}^{\text{2}}$ .

Calculation:

The expression for the area of the function in square feet is:

  $A\left(b\right)=1200b$

Number of bags of grass seed are $8$ . So, the number of bags is the require domain. So, the domain for number of bags is:

  $D:\left\{b|0\le b\le 8\right\}$

Since the domain ranges for $0$ to

  $8$ , therefore, range for $A$ will be also from $0$ to $8$ .

To calculate area for $1$ number of bag, substitute $1$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(1\right)=1200\left(1\right)\\ A=1200\end{array}$

To calculate area for $2$ number of bags, substitute $2$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(2\right)=1200\left(2\right)\\ A=2400\end{array}$

To calculate area for $3$ number of bags, substitute $3$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(3\right)=1200\left(3\right)\\ =3600\end{array}$

To calculate area for $4$ number of bags, substitute $4$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(4\right)=1200\left(4\right)\\ =4800\end{array}$

To calculate area for $5$ number of bags, substitute $5$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(5\right)=1200\left(5\right)\\ =6000\end{array}$

To calculate area for $6$ number of bags, substitute $6$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(6\right)=1200\left(6\right)\\ =7200\end{array}$

To calculate area for $7$ number of bags, substitute $7$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(7\right)=1200\left(7\right)\\ =8400\end{array}$

To calculate area for $8$ number of bags, substitute $8$ for $b$ in the above given expression.

  $\begin{array}{c}A\left(8\right)=1200\left(8\right)\\ =9600\end{array}$

The range for area for $8$ number of bags is:

  $R:\left\{A|0\le A\le 9600\right\}$

Therefore, the domain of $b$ will range from $D:\left\{b|0\le b\le 8\right\}$ and the range of $A$ will range from $R:\left\{A|0\le A\le 9600\right\}$ .