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 = 35t + 300 ) gives ( w ) as a function of ( t ) during the next 80 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.

description of values	domain:	range:
set of values	select ( \boldsymbol{downarrow} )	select ( \boldsymbol{downarrow} )

Explanation:

Step1: Define domain (input variable)

The function $W=35T+300$ takes $T$ (minutes water added) as input. The time period is 0 to 80 minutes, so the domain is the set of values $0 \leq T \leq 80$, which corresponds to the number of minutes water has been added.

Step2: Define range (output variable)

The output is $W$, the total amount of water in liters. Calculate the minimum and maximum $W$:
Minimum (when $T=0$): $W=35(0)+300=300$
Maximum (when $T=80$): $W=35(80)+300=2800+300=3100$
So the range is the set of values $300 \leq W \leq 3100$, which corresponds to the amount of water in the pond (in liters).

Answer:

Domain: Number of minutes water has been added
Range: Amount of water in the pond (in liters)