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Math Help - Fractional Exponents, functions

  1. #1
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    Fractional Exponents, functions

    A bacteria culture starts with 500 bacteria and doubles in size every 30 minutes. Graph the population function and estimate the time for the population to reach 20,000.

    So far I did 20,000/500 = 2^(x/30)
    which is 40= 2^(x/30)
    now how do i get rid of the fractional exponent (x/30)??
    -----------------------------
    Also if g(x) = 4 + x + e^x
    find g^-1 (5)
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  2. #2
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    Quote Originally Posted by rafaeli View Post
    A bacteria culture starts with 500 bacteria and doubles in size every 30 minutes. Graph the population function and estimate the time for the population to reach 20,000.

    So far I did 20,000/500 = 2^(x/30)
    which is 40= 2^(x/30)
    now how do i get rid of the fractional exponent (x/30)??
    -----------------------------
    Also if g(x) = 4 + x + e^x
    find g^-1 (5)
    Are you familiar with logarithms? Starting with 40=2^{\frac{x}{30}}, now take the natural log of both sides and you get \ln(40)=\ln{ \left( 2^{\frac{x}{30}} \right)}

    Now to get rid of that exponent, use a rule that says \ln(a^n)=n\ln(a) Thus \ln(40)=\frac{x}{30} \ln(2).

    Are you with me so far?
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  3. #3
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    Thank you. I got that part. Took me a while to understand it but I finally got it.
    Now i want to know like how many bacteria are there after t hours?
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