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    • Thread Starter

    This is the question:
    A trading company made a profit of £50,000 in Year 1
    A model for future trading predicts that profits will increase year by year in a geometric sequence with common ratio r, r>1

    The model predicts that in Year n, the profit made will exceed £200,000

    Show that n > (log 4)/(log r) + 1

    I have no clue how to do this question...please help!

    Thank you in advance.
    • Thread Starter


    A geometrical sequence is one where the next term is found by multiplying the previous term by a constant multiplier, r.

    So the sequence is:

    a, ar, ar^2, ar^3, ..., ar^n.

    Note that the first term a = £50,000 is year one and the power of r I would have put in the above sequence is zero if I didn't omit it for simplicity.

    Therefore, in each term r is raised to the power of (n - 1) where n is the year number.

    To exceed £200,000,

    ar^{(n-1)} > 200, 000

    You can then log both sides to bring (n-1) down and use the log rules to rearrange to give the final answer.

    Hope that helped.
    • Thread Starter

    I understand now!
    Thank you
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Updated: March 16, 2011

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