1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Derivative and water flow

  1. Jan 31, 2008 #1
    1. The problem statement, all variables and given/known data

    Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 6.00t 0.8 - 3.35t + 23.00, with t 0, m in grams, and t in seconds.
    (a) At what time is the water mass greatest?

    (b) What is that greatest mass?

    (c) In kilograms per minute, what is the rate of mass change at t = 2.00 s?

    (d) In kilograms per minute, what is the rate of mass change at t = 5.00 s?
    2. Relevant equations
    The first derivative would be 4.8t^-.2-335

    3. The attempt at a solution

    a)I set the derivative equal to zero and figured t to be 2.3375, but it says thats wrong.
    b)I assume I'd plug a into the original and try tht, but I can't get a.
    c and d)I tried to put 2 and 5 into t as the origional, but they are not right.
  2. jcsd
  3. Jan 31, 2008 #2
    a) is, as you said, the solution for t when


    However, the solution to


    is not 2.3375, check your algebra.

    b), as you said is [tex]m(t)[/tex] for the solution above
    c) and d) can both be found by substituting the times into the expression for [tex]\frac{dm}{dt}.[/tex]
  4. Jan 31, 2008 #3
    Thanks. Where did the 3.35 come from? How would I solve t^-.2?
  5. Feb 1, 2008 #4
    The 3.35 is from the original expression for m, unless you've mistyped it. I used logarithms and the change of base rule to solve for t.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook