The number of gallons in a wading pool that is being drained. Using the points (1, 160) and (3, 80), what is the rate of change in the number of gallons in the pool after each hour has passed?
A. −40 gal./hr.
B. 40 gal./hr.
C. −140 gal./hr.
D. 140 gal./hr.
The bot assumed that for the given points, the change in y represents the change in the number of gallons in the pool, and the change in x represents the time in hours.
Nowhere did it say that
The bot made an error in finding the slope.
You must take the difference in the same direction, that is,
(y2 - y1)/(x2 - x1) , the bot did (y1 - y2)/(x2 - x1)
the result should have been
- 40
the "-" shows that the volume was decreasing, in the bot's answer the
pool would be filling up, not draining
The rate of change can be found using the slope formula:
slope = (change in y) / (change in x)
In this case, the change in y represents the change in the number of gallons in the pool, and the change in x represents the time in hours.
The change in y is 160 - 80 = 80 gallons.
The change in x is 3 - 1 = 2 hours.
Plugging these values into the slope formula:
slope = (80 gallons) / (2 hours) = 40 gallons/hour
Therefore, the rate of change in the number of gallons in the pool after each hour has passed is 40 gal./hr.
The correct answer is B.
Thank you for pointing that out. You are correct that in this context, the change in y represents the change in the amount of water in the pool, and the change in x represents the time in hours. The slope formula should be used with (y2 - y1)/(x2 - x1), not (y1 - y2)/(x2 - x1).
Using (y2 - y1)/(x2 - x1) with the given points (1, 160) and (3, 80):
slope = (80 - 160) / (3 - 1) = -80/2 = -40
Therefore, the rate of change in the number of gallons in the pool after each hour has passed is -40 gal./hr, as the pool is being drained.
The correct answer is A.
To find the rate of change in the number of gallons in the pool after each hour has passed, we need to calculate the slope of the line passing through the given points.
First, let's assign the coordinates (x1, y1) = (1, 160) and (x2, y2) = (3, 80).
The formula to calculate the slope of a line passing through two points is:
slope = (change in y)/(change in x)
In this case, the change in y is y2 - y1, and the change in x is x2 - x1.
change in y = 80 - 160 = -80
change in x = 3 - 1 = 2
Therefore, the slope is: slope = (-80)/(2) = -40
The slope represents the rate of change in the number of gallons in the pool after each hour has passed. Since the slope is negative, it means that the number of gallons in the pool is decreasing at a rate of 40 gallons per hour.
Hence, the correct answer is A. -40 gal./hr.