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.

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Presentation transcript:

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

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.

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

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?

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

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

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= minutes constant temperature of the room