A city is working to fill a pond. The pond can hold 10,000

Question

gallons of water. The pond currently has 1,000
gallons of water and they are adding 50
gallons of water per minute. Let W
represent the amount of water in the pond (in gallons) and m
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
w(m)=50m+1000.
What is the unit used and a reasonable scale for the variable W

?
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
.

Answer 1

The situation describes the amount of water in the pond in gallons. The function \( W(m) = 50m + 1000 \) indicates that as time in minutes increases, the amount of water \( W \) in the pond also increases.

Given that the pond can hold up to 10,000 gallons and currently has 1,000 gallons, the pond will be filled when the water reaches that maximum capacity.

A reasonable scale for \( W \) (the amount of water in the pond) can be increments of 1,000 gallons, matching the significant levels of water in the pond.

Thus, the responses can be summarized as follows:

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

This choice fits within the bounds of the pond's capacity while making it easy to visualize the water level changes over time.