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Math Help - exponential word problem

  1. #1
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    exponential word problem

    I need a little help as to how to start this one.


    At noon, the population of a bacterial culture was 2.4 x 10^6. At 4pm., the population was 6.2 x 10^7. Assume exponential growth. When will the population be 8.2 x 10^8?
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  2. #2
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    Try the model P=P_0e^{kt}

    With P = population and t = hours

    you can say for (t,P) = (0,2.4 \times 10^6)

    therefore P_0 = 2.4 \times 10^6

    P=2.4 \times 10^6\times e^{kt}

    Now use (t,P) = (4,6.2 \times 10^7) to solve for k and you will have your model

    After this 8.2 \times 10^8 goes into the model for P, solve for t.

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