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
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