College Algebra

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Quadratic Function problem:

When a certain drug is taken orally, the concentration of the drug in the patients bloodstream after t minutes is given by C(t)=0.06t-0.0002t^2, where 0 ≤ t ≤ 240 and the concentration is measured by mg/L. When is the maximum serum concentration reached, and what is that maximum concentration?

  • College Algebra -

    Take the derivative,set equal to zero, solve for time.

    C'=0=.06-.0004t

    t= solve.
    Then put that t in the C(t) to find max concentration.

  • College Algebra -

    Ooops. I just realized you have not had calculus yet.\

    Here is your way.

    solve for the roots (when C=0)

    0=.06t-.0002t^2=t(.06-.0002t)
    or t=0, and t= .06/.0002

    because the max has to be at the midpoint of these two roots (qudratics plot symettrically), the the max occurs between 0 and .06/.0002 or .06/.004. Use that time to solve for C(t)

  • College Algebra -

    In class we were given formulas such as:
    f(x)= ax^2 + bx+ c
    x= -b/2a
    and then an f(x) or whatever the letters are being used in the word problem where you plug in the answer for x back into the original equation. I just don't understand what role the 0 ≤ t ≤ 240 comes in because we haven't done any like this in class yet but it was assigned for hw! help?

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