water flows into a reservoir at a rate of 1500+7t^2 gallons/hour. Since there is a tiny hole in the reservoir, the water leaks out at a rate of 4t+t^2 gallons/hour. What is the net change in the amount of water in the reservoir over the time interval of [1,5]

9514 1404 393

  6200 gallons

Step-by-step explanation:

The rate of change of volume is the difference between the inflow rate and the outflow rate.

  v'(t) = (1500 +7t^2) -(4t +t^2) = 6t^2 -4t +1500

The change in volume over the time interval of interest is the integral of this expression over that interval:

The amount of water in the reservoir increases by 6200 gallons over the time interval.

a

b

d

step-by-step explanation: