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Published byHorace Hawkins Modified over 9 years ago
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OBJECTIVES: FIND EQUATIONS OF POPULATION THAT OBEY THE LAW OF UNINHIBITED GROWTH AND DECAY USE LOGISTIC MODELS Exponential Growth and Decay; Logistic Models
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Exponential Growth or Decay Model is the original amount, or size, of the entity at time, is the amount at time and is the a constant representing either the growth or decay rate. If, the function models the amount, or size, of a growing entity. If, the function models the amount, or size, of a decaying entity GrowthDecay
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a) DETERMINE THE NUMBER OF INSECTS AT DAYS b) WHAT IS THE GROWTH RATE OF THE INSECT POPULATION? c) WHAT IS THE POPULATION AFTER 10 DAYS? EX: Growth of an Insect Population: The size P of certain insect population at time t (in days) obeys the function
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d) When will the (number) insect population reach 800? e) When will the insect population double? d) e)
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EX: Radioactive Decay Strontium 90 is a radioactive material that decays according to the function, where is the initial amount present and is the amount present at time (in years). Assume that a scientist has a sample of 500 grams of Strontium 90. a) What is the decay rate of Strontium 90? b) How much Strontium 90 is left after 10 years?
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Radioactive Decay c) When will 400 grams of Strontium 90 be left? d) What is the half-life of Strontium 90?
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Population Growth The population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population is 10,000, what will the population be 2 years from now? -
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Logistic Growth Model The mathematical model for limited logistic growth is given by The value of P can never exceed c and c represents the limiting size that A can attain.
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Proportion of the Population that owns a DVD The logistic growth model relates the proportion of U.S. households that own a DVD to the year. Let represent 2004, represent 2005, and so on. a) What proportion of the U.S. households owned a DVD in 2004? b) Determine the maximum proportion of households that will own a DVD
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c) When will 0.8 (80%) of U.S. households own a DVD? -
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