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Average Rate of Change Using MVT for Derivatives

  1. Mar 27, 2009 #1
    1. The problem statement, all variables and given/known data

    The mass, m(t), in grams, of a tumor t weeks after it begins growing is given by m(t) = [te^t] / 80 .

    What is the average rate of change, in grams per week, during the fifth week of growth?

    a.) 2.730
    b.) 3.412
    c.) 6.189
    d.) 6.546
    e.) 11.131

    2. Relevant equations

    The Mean Value Theorem (MVT) for Derivatives states that the average rate of change between two points is the secant line between those two points given by the equation:

    f ( b ) - f ( a ) / b - a

    3. The attempt at a solution

    Since m(t) is the mass of the tumor, and we're looking for average rate of change (the slope of the secant line), we must use the MVT for derivatives.

    I performed the following calculation:

    m (5) - m(0) / 5 - 0 .... but got 1.8555.... not one of the answer choices.

    Is my logic wrong?
     
  2. jcsd
  3. Mar 27, 2009 #2

    Mark44

    Staff: Mentor

    Yes, your logic is wrong. You want the average rate of change during the 5th week; i.e., between the start of week 4 and week 5. Try [m(5) - m(4)]/1. The value I get is one of those given.
     
  4. Mar 27, 2009 #3
    Hi Mark44. Thank you for your quick response. Why do we find the average from the 4th week and 5th week instead of the 0th week and the 5th week? I'm having trouble grasping that concept.

    I plugged it back in and get an answer of 6.546.

    Thanks
     
  5. Mar 27, 2009 #4

    Mark44

    Staff: Mentor

    This means from t = 4 weeks through t = 5 weeks.

    What you did was the average rate of change for the first 5 weeks, not for the fifth week.

    IIRC, 6.546 is what I got.
     
  6. Mar 28, 2009 #5
    Thanks Mark
     
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