2005 Free Response

1. The amount of sand being removed from the sand is represented by the integral or anitderivative of R(t).

2. From the given we know that the beach contains 2500 cubic yards of sand when t=0.To find the amount of sand in a given time we need to know the net change of sand meaning the amount of sand leftover when sand is being removed. When finding the change we then just add it to the initial amount of 2500. The integral of S(t) is the amount of sand being added and the integral R(t) is the amount of sand being removed.
3. The rate at which the amount of sand on the beach is changing can be calculated by the formula S(t)-R(t). S(4)-R(4)= 1.909 cubic yards/hrs.

4. To find were where the sand on the beach is at its minimum we graph the equation S(t)-R(t) and find the x-interceps. The minimum is where t=5.118 since t=o,6 are both maximums. To find the minimum value we input t=5.118 into the equation Y(5.118)=2500+fnint (S(t)-R(t),t,0,5.118) which comes up to be 2492.369 cubic yards.