Question

The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that w=5T+300 gives W as a function of T during the next 70 minutes.Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.

Answer 1

Given:

The function is:

`W=35T+300`
`\begin{gathered} W=\text{ Total amount of water} \\ \\ T=\text{ Time} \end{gathered}`

Find-:

(a)

Domain

(b)

Range

Explanation-:

(a)

Domain-: The domain defines all possible input real values of a function

The input of the function is time and time is 70 min

so,

Domain is:

`=\text{ Number of minutes water has been added}`

The value of the domain is

`=\text{ The set of all real numbers }0\text{ to }70`

Range

The range is all output values for the domain

So, the range is:

`W=35T+300`

At t = 0 domain is:

`\begin{gathered} W=35T+300 \\ \\ W=35(0)+300 \\ \\ W=300 \end{gathered}`

At T = 70 the water is:

`\begin{gathered} W=35T+300 \\ \\ W=35(70)+300 \\ \\ W=2450+300 \\ \\ W=2750 \end{gathered}`

The range is 30 to 2750

The range is :

`\text{ Amount of water in the pond }`

The value of the range is:

`\text{ The set of all real numbers from }300\text{ to }2750`