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Math Help - Exponential Decay

  1. #1
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    Exponential Decay

    A lab culture initially contains 500 bacteria. Two hours later, the number of bacteria has decreased to 200. Find the exponential decay model of the form
    B=B_0a^{kt}
    that can be used to approximate the number of bacteria after t hours.
    I have no idea where to start. Any ideas?
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  2. #2
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    B_0 is the initial population at t = 0 ... which is 500.

    you were given another point on the curve , (2,200)

    so, sub in 200 for B and 2 for t ... solve for k.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    B_0 is the initial population at t = 0 ... which is 500.

    you were given another point on the curve , (2,200)

    so, sub in 200 for B and 2 for t ... solve for k.
    What would you sub in for a though?

    Cause when I substitute what you said, I get the equation 200 = 500a^{2k} and when I solve for k, I get k = \frac {log_a\frac{2}{5}}{2}. What would a be?
    Last edited by chrozer; November 30th 2008 at 06:15 PM.
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  4. #4
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    "a" can be any positive value you want that doesn't equal 1.

    I'd use "e" since it's calculator friendly.
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  5. #5
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    Quote Originally Posted by skeeter View Post
    "a" can be any positive value you want that doesn't equal 1.

    I'd use "e" since it's calculator friendly.
    Ok thanks alot. I finally got it.
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  6. #6
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    Re: Exponential Decay

    Quote Originally Posted by chrozer View Post
    Ok thanks alot. I finally got it.
    What is the final answer? -.458?
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  7. #7
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    Re: Exponential Decay

    I'd use "e" since it's calculator friendly.

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