A city is working to fill a pond. The pond can hold

Question

gallons of water. The pond currently has
gallons of water and they are adding
gallons of water per minute. Let
represent the amount of water in the pond (in gallons) and
represent the time, in minutes, the city workers have been working to fill the pond with more water. The function that represents the situation is
.
What is the unit used and a reasonable scale for the variable
?
Responses

The unit used is gallons and a reasonable scale would be increments of
, from
to
.
The unit used is gallons and a reasonable scale would be increments of 1 comma 000, from 0 to 10 comma 000.

The unit used is minutes and a reasonable scale would be increments of
, from
to
.
The unit used is minutes and a reasonable scale would be increments of 1, from 0 to 180.

The unit used is gallons and a reasonable scale would be increments of
, from
to
.
The unit used is gallons and a reasonable scale would be increments of 10, from 0 to 10 comma 000.

The unit used is minutes and a reasonable scale would be increments of
, from
to
.
The unit used is minutes and a reasonable scale would be increments of 10, from 0 to 180.

Answer 1

To determine the correct response, we need to focus on the variables represented in your scenario. The variable \( t \) represents time in minutes, and the variable \( W \) represents the amount of water in gallons.

1. The unit for the variable \( W \) (amount of water in the pond) is gallons.
2. The unit for the variable \( t \) (time spent filling the pond) is minutes.

Given the context, a reasonable scale for each variable would depend on the total volume of the pond and the rate at which water is being added.

Assuming a typical pond could hold a relatively large amount of water (let's say 10,000 gallons), and you might be adding water at a practical rate (for example, 10 gallons per minute), calculations will carry over from the variables of gallons into minutes, leading us to a reasonable scale.

Thus the responses can be weighed as follows:

• The unit used for the amount of water is gallons. A reasonable incremental scale of gallons could be increments of 1,000, spanning from 0 to 10,000, which provides a clear view of water volume in a reasonably large pond.

• For the time variable (minutes), a more granular approach, like increments of 10 minutes, ranging from 0 to 180 minutes, may be appropriate depending on the full operational timeframe to fill the pond.

Based on those analyses, the most appropriate selected response is:

The unit used is gallons, and a reasonable scale would be increments of 1,000, from 0 to 10,000.

This scale for gallons aligns with how water volumes would typically be quantified in a project that aims to fill a pond effectively.