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Finding the AVG ROC for this problem

  1. Apr 3, 2013 #1
    1. The problem statement, all variables and given/known data

    With an initial deposit of $100, the balance in a bank account after t years is f(t)=100(108)t dollars.
    Find the average ROC over the intervals of [0, 0.5] and [0, 1]

    2. Relevant equations

    It first describes in the book the manner in which you solve this problem as such:
    Δf= f(x1)-f(x0), Δx=x1-x0
    So you calculate the first one, then divide it by the calculated result of the second one

    In the book, it gives this example.
    --Compute the avg ROC of v with respect to T over the interval [273,300].
    Δv/Δt = (20√300 - 20√273)/(300-273) ≈ 15.95/27 ≈ 0.59 m/s per K

    3. The attempt at a solution

    So, I had already solved a problem for avg ROC using that formula and it was correct. Now, given that the answer to my current problem is in the back of the book, I cannot seem to match it.

    My attempt for the ordered pair [0, 0.5] is as follows:

    f(t) = 100(108)0.5-100(108)0
    Any number to the power of zero = 1, therefore:
    100(108)0.5-100(1)
    1,039.230485 - 100 = 939.2304845
    This would be the upper half, then divide this by the lower half, or x1-x0
    which is 0.5 - 0...so

    939.2304845 / 0.5 = 1,879.460969. The book gives the answer as 7.8461 for just that ordered pair. Once I figure out where I went wrong, I can figure out the second ordered pair. Appreciate any help.

    EDIT: Wow I feel stupid. Ok, well, it is 1.08, not 108. Fixing that, and I get the right answer. Carry on, nothing to see here.
     
    Last edited: Apr 3, 2013
  2. jcsd
  3. Apr 3, 2013 #2

    Mark44

    Staff: Mentor

    ROC = rate of change?
     
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