The tide removes the sand from a beach at a rate modeled by the function R, given by . A pumping station adds sand to the beach at a rate modeled by the function S, given by .
Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for . At time , the beach contains 2500 cubic yards of sand.
How much sand will the tide remove from the beach during this 6 hour period. Indicate units of measure. Write an expression for the total number of cubic yards of sand on the beach at time t.
Any help is appreciated, thanks.
I knew this looked familiar. It's from the AP Calculus AB 2005 Free Response questions. I'm feeling a little too lazy to solve this right now, but if you Google "Lou Talman" you'll find the answer to this question and a lot others (so I can be justifiably called efficient instead of lazy...yeah, that's it).
He only gives solutions but the questions themselves can all be found on the AP site.