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Water is flowing into a pond (cubic inches per hour) at the varying rates given below.

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Water is flowing into a pond (cubic inches per hour) at the varying rates given below.
Time of Day  |  10:00 AM  |  10:15 AM  |  10:30 AM  |  10:45 AM  |  11:00 AM
Flow (in3/h)  |  14              |  10             |   7               |  6               |   7

A. Using left endpoint rectangles, estimate the average flow rate from 10:00 AM until 11:00 AM.

B. Using right endpoint rectangles, estimate how much water flows into the pond from 10:00 AM until 11:00 AM.

C. Suppose we are given the following model for the flow rate f(x)=13.71x^2-20.91x+14.11 with x = 0 corresponding to 10:00 AM and x = 1 corresponding to 11:00 AM. If there is also water flowing out of the pond at a rate of g(x)=x^2-2x+4 , what is the net change in water from 10:00 AM to 11:00 AM?

Appreciate the help

Apr 23, 2020

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A    Use the average     for  1 hour    (14 +7)/2 = 11.5 in3/hr

B not sure what this means   but I believe     11.5 in^3/hr x 1 hr = 11.5 in3

C.   Not sure what 'net change in water' means

but maybe this      f(x) - g(x)      find values for x = 0    then subtract the values of  x = 1

at 0   f(x)  = 14.11    g(x) = 4        14.11 - 4 = 10.11

at 1 (f(x) = .....         g(x) = ......                   =.........

10.11 - ....... =  net flow rate change from 10 to 11

Apr 23, 2020