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Math Help - Looking for ideas on this.

  1. #1
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    Looking for ideas on this.

    Hi, I am currently struggling with Logarithms and exponentials in pre calc. the two in particular are f(x)=-2+logbase 1/2(x+2) sketch the graph and identify domain range x/Y intercept and end behaivor. and

    In mediaeval times there were 10,000 people living in a city that was struck by a plague. the number of people living after 6 days was 8500, and after 12 was 7225 explain how you determine it is exponential and fill in a table and find an equation/common ratio.

    Thanks a lot for any ideas or help for on where to start.
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  2. #2
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    Re: Looking for ideas on this.

    f(x) = -2 + \log_{\frac{1}{2}}(x+2)

    note that you can change the base ...

    \log_{\frac{1}{2}}(x+2) = \frac{\log_2(x+2)}{\log_2\left(\frac{1}{2}\right)} = -\log_2(x+2)

    f(x) = -2 - \log_2(x+2) = -[2 + \log_2(x+2)]

    domain ...

    x+2 > 0 \implies x > -2

    range would be all reals

    y-intercept ... evaluate f(0)

    x-intercept ... f(x) = 0 \implies \log_2(x+2) = -2

    graph will be the function y = 2 + \log_2(x+2) reflected over the x-axis


    second problem ... \frac{8500}{10000} = 0.85 , what is the value of \frac{7225}{8500} ? does that tell you something?
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  3. #3
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    Re: Looking for ideas on this.

    and after achieving a common factor getting my equation would be something like your common factor raised^x power? wasn't very good at it.
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  4. #4
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    Re: Looking for ideas on this.

    Quote Originally Posted by Jimbo32 View Post
    and after achieving a common factor getting my equation would be something like your common factor raised^x power? wasn't very good at it.
    so, let's cut the self-deprecation ... what is the equation you came up with?
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  5. #5
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    Re: Looking for ideas on this.

    I got something like 2*.85^X but I dont know if i did it right. I took the difference in the days 12/6 which was two and multiplied that by my common factor and raised it to X because that was changing. though that doesnt seem right.
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  6. #6
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    Re: Looking for ideas on this.

    Quote Originally Posted by Jimbo32 View Post
    I got something like 2*.85^X but I dont know if i did it right. I took the difference in the days 12/6 which was two and multiplied that by my common factor and raised it to X because that was changing. though that doesnt seem right.
    every six days, the population decreases by 15%

    population as a function of time , t , in days ...

    P(t) = 10000(0.85)^{\frac{t}{6}}

    ... you really need to have a sit-down with your instructor or a real live tutor.
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