SOLUTION: During a nine hour storm it snows at a rate of 1 inch per hour for the first two hours, at a rate of 2 inches per hour for the next six hours, and at a rate of 1 inch per hour for

Algebra ->  Functions -> SOLUTION: During a nine hour storm it snows at a rate of 1 inch per hour for the first two hours, at a rate of 2 inches per hour for the next six hours, and at a rate of 1 inch per hour for       Log On


   

Question 388569: During a nine hour storm it snows at a rate of 1 inch per hour for the first two hours, at a rate of 2 inches per hour for the next six hours, and at a rate of 1 inch per hour for the final hour. Write and graph a compound function that gives the depth of snow during the snowstorm.
Not sure which section this would be in... I know this says no graph but I can probably figure out the graph on my own anyways.
Any help at all is appreciated greatly!
Happy holidays :)
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
Recall the equation of a line, y=mx+b. We will be using a similar equation, but with snow, S, and time, t instead of y and x.

The rate of inches per hour represents the slope of the graph, m.
The y-variable would be the amount of snow, S.
The x-variable would be the time, t, in hours.

The function has three pieces:

i) S = t (slope = 1)
ii) S = 2t (slope = 2)
iii) S = t (slope = 1)

For the first piece, i), t=2, so the amount of snow is 2 inches.
For the second piece, ii) t=6, so the amount of snow is 12 inches.
For the third piece, iii) t=1, so the amount of snow is 1 inch.

In total, it snowed 15 inches.

Hopefully this makes sense. The graph is just three lines. The first and third pieces are identical, while the middle piece is a bit steeper, with a slope of 2.