mac1140_lecture25_1

# mac1140_lecture25_1 - L25 5.6 Exponential Growth or Decay...

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221 L25 § 5.6 Exponential Growth or Decay In many situations, the quantity changes at a rate proportional to the amount present. For example, 0.023 80,000 t Pe = could represent the population of Gainesville t years from 1990. At this rate we could estimate the population in the year 2010:

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222 Exponential Growth or Decay: Let 0 y be the amount or number present at time 0 t = . Then the amount present at time t is kt e y y 0 = , where k is a constant. Example . The number of bacteria in a sample culture is given by the formula ( t is in hours) (ln 2) / 2 500 t ye = . a) How many bacteria were initially in the culture? b) What is the number of bacteria at the end of 3 hours? c) How long does it take for the number to increase to 5000?
223 Half-life: The time it takes for a quantity that decays exponentially to become half its initial amount. Doubling Time: The time it takes for a quantity that grows exponentially to become twice its initial amount. Example : Find the half-life of iodine-131 (used in the diagnosis of the thyroid gland) if it decays according to

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mac1140_lecture25_1 - L25 5.6 Exponential Growth or Decay...

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