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EXPONENTIAL GROWTH & DECAY; Application

EXPONENTIAL GROWTH & DECAY; Application. In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential growth model in which t is the number of years after 2000, to find the exponential growth function that models the data . The model is.

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EXPONENTIAL GROWTH & DECAY; Application

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  1. EXPONENTIAL GROWTH & DECAY; Application In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential growth model in which t is the number of years after 2000, to find the exponential growth function that models the data. • The model is

  2. Application continued:- • By which year will Africa’s population reach 2,000 million. Use the exponential growth function model: to find how long it will take to reach a population of 2,000 million.

  3. Exponential Decay APPLICATION • The half-life of strontium-90 is 28 years, meaning that after 28 years a given amount of the substance will have decayed to half the original amount. Find the exponential decay model for strontium-90

  4. APPLICATION CONTD. • We found the exponential decay model to be If there are originally 60 grams, how long will it take for strontium-90 to decay to a level of 10 grams?

  5. Example of Exponential Decay • The half-life of thorium-229 is 7340 years. How long will it take for a sample of this substance to decay to 20% of its original amount? • Use formula

  6. Logistic Growth Model

  7. Logistic Growth Model • In a learning theory project, psychologists discovered that • is a model for describing the proportion of correct responses, f(t), after t learning trials. Find the proportion of correct responses prior to learning trials taking place. • Prior to learning trials taking place, the proportion of correct responses was 0.4

  8. Newton’s Law of Cooling

  9. Newton’s Law of Cooling • An object is heated to 100°C. It is left to cool in a room that has a temperature of 30°C. After 5 minutes, the temperature of the object is 80°C. Use Newton’s Law of Cooling to find a model for the temperature of the object, T, after t minutes. • initial temperature time = 5 min • temperature after T= 30 + 70 • 5 minutes constant temperature of the room

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