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Math Help - Tide removing sand from a beach

  1. #1
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    Tide removing sand from a beach

    The tide removes the sand from a beach at a rate modeled by the function R, given by R(t) = 2+5sin\frac{4*pi*t}{25}. A pumping station adds sand to the beach at a rate modeled by the function S, given by S(t)=(15t)/(1+3t).

    Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for 0=<t=<6. At time t=0, 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.
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  2. #2
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    Quote Originally Posted by lancelot854 View Post
    The tide removes the sand from a beach at a rate modeled by the function R, given by R(t) = 2+5sin\frac{4*pi*t}{25}. A pumping station adds sand to the beach at a rate modeled by the function S, given by S(t)=(15t)/(1+3t).

    Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for 0=<t=<6. At time t=0, 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.
    sand removed from the beach in 6 hrs ... \displaystyle \int_0^6 R(t) \, dt

    total sand on the beach at time t ... \displaystyle 2500 + \int_0^t S(x) - R(x) \, dx

    both accumulation functions will have units in cubic yards of sand.
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  3. #3
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    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.
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