Answer:
A) 12 is the miles from Paul's work to his home.
B) It takes Paul 48 minutes to go from work to home.
C) A reasonable domain would be 32 to 96 minutes.
Explanation:
The distance from home in miles, D(t), is given by the function D(t) = 12 -
0.75t, where t is time, in minutes.
Build a table:
Time(min) Miles From Home (D(t))
1 11.25
2 10.50
3 9.75
4 9.00
5 8.25
The 12 in the equation (D(t) = 12 - 0.25t) is the miles from work to home. At t = 0, Paul is 12 miles from home.
We can find the time it takes for Paul to reach home by setting D(t) equal to 0 (he's 0 miles from home, so to speak) and solving for t:
D(t) = 12 - 0.25t
0 = 12 - 0.25t
-0.25t = -12
t = 48 minutes
The 0.25 is Paul's speed, in miles/minute. 0.25 miles/minute is a little slow. Lets convert it to miles per hour, which is a more relatable unit.
(0.25 miles/min)*(60 minutes/1 hour) = 15 miles/hour
We can imagine Paul's drive home is in a city, and has stop lights, heavy traffic, and speed cops.
A reasonable domain for this function would include all values of time (x axis) that one could possibly anticipate for a 12 mile drive. A person walks 3 miles/hour That would mean 4 hours to go 12 miles. Since this is a car, the domain is likely much smaller, although one needs to consider traffic and stops (stop signs and lights, and police). A speed of 60 miles/hour is 1 mile/minute. This is likely too fast (12 minutes to go 12 miles).
If we allow speed changes of up to 50% either faster or slower, Paul's commute home would range from 32 to 96 minutes. A reasonable domain would be 32 to 96 minutes.