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Math Help - Some help with sequences and functions?

  1. #1
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    Smile Some help with sequences and functions?

    So on my homework, there is a question that says:

    Is it possible for the sequence t(n)=5*2^n to have a term with the value of 200? If so, which term is it? If not, justify your answer.


    and another


    Is it possible for the function f(x)=5*2^x to have an output of 200? if so, what input gives this output? If not, justify your answer.


    If you do decide to help, show your work and explain why/why not please thanks.
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  2. #2
    Member HappyJoe's Avatar
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    Notice also that the sequence t is really just a special case of f. That is f(n) = t(n) for all natural numbers n.

    Hence it suffices to find all x, for which f(x) = 200, and check if any of these x are integers. The function f is strictly increasing: This means that when x gets larger, the value f(x) also gets larger. This means in turn that there can be at most one value of x, for which f(x) = 200. What is this value? You need to solve the equation

    5*2^x = 200

    for x. First divide both sides by 5 to get

    2^x = 40.

    Do you know logarithms? If you do, use them to find x. You will get x = log(40)/log(2) (be sure to understand this (but only if you know logarithms)). This value of x is not an integer.
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