Snowfall Suppose 5 inches of snow fall before noon
and 2 inches per hour fall thereafter until 10 P.M.
(a) Write a formula that calculates the snowfall S in
inches, x hours past noon.
(b) Use your formula to calculate the total snowfall
at 8 P.M.
(c) How much snow had fallen at 6:15 P.M.?
s = 5 + 2x 0 <= x <= 10
plug in x=8 or x=6.25 for the other parts.
S=4.5
To calculate the snowfall, we need to analyze the information provided and come up with a formula to represent the snowfall at any given time. Let's break it down step by step.
(a) The snowfall before noon is given as 5 inches. After noon, the rate of snowfall is 2 inches per hour until 10 P.M. To calculate the snowfall in inches, x hours past noon, we can use the following formula:
S = 5 + 2(x - 12)
In this formula, S represents the snowfall in inches, x represents the number of hours past noon. We subtract 12 from x to account for the time before noon, so that x - 12 represents the time after noon.
(b) To calculate the total snowfall at 8 P.M., let's plug in x = 20 (8 P.M. is 8 hours past noon) into the formula:
S = 5 + 2(20 - 12)
S = 5 + 2(8)
S = 5 + 16
S = 21
Therefore, the total snowfall at 8 P.M. is 21 inches.
(c) To find out how much snow had fallen at 6:15 P.M., we can calculate the snowfall for 6:15 P.M., which is 6 hours and 15 minutes past noon. We need to convert the time into a decimal representation. Since there are 60 minutes in an hour, 15 minutes is equivalent to 15/60 = 0.25 hours. Therefore, the total time in hours is 6 + 0.25 = 6.25.
Now, let's substitute x = 6.25 into the formula:
S = 5 + 2(6.25 - 12)
S = 5 + 2(-5.75)
S = 5 - 11.5
S = -6.5
Since we can't have negative snowfall, we interpret this result as no snowfall at 6:15 P.M.
Therefore, at 6:15 P.M., no snow had fallen.