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Math Help - exponential growth/decay word problem

  1. #1
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    exponential growth/decay word problem

    When exposed to sunlight, the # of bacteria in a culture decreases exponentially at the rate of 10% per hour. What is the best approximation for the number of hours required for the initial # of bacteria to decrease by 50%.
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  2. #2
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    Quote Originally Posted by cityismine View Post
    When exposed to sunlight, the # of bacteria in a culture decreases exponentially at the rate of 10% per hour. What is the best approximation for the number of hours required for the initial # of bacteria to decrease by 50%.
    Let A(0) denote the initial amount of bacteria and A(t) the amount of bacteria after t hours of exposion to sun light.

    After 1 h there remains 90% of the bacteria. After t hours remains 0.9^t of the bacteria.

    You know that \frac{A(t)}{A(0)}=\frac12

    Use the equation

    A(t) = A(0) \cdot (0.9)^t

    plug in the values you know and solve for t.

    I've got t is roughly 6h 35 min
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    Learning to translate is the point, here.

    "# of bacteria in a culture"

    Define this. B(t) = # of bacteria in a culture - at time t in hours.

    "decreases exponentially"

    A clue about B(t) = ae^{bt}

    "decreases exponentially at the rate of 10% per hour."

    A clue about the parameter: B(1) = ae^{b} = 0.90*ae^{0} = B(0)

    "number of hours required for the initial # of bacteria to decrease by 50%."

    B(x) = 0.90^{x} = 0.50 -- Solve for x.
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