Sullivan PreCalculus Section 4

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Presentation transcript:

Sullivan PreCalculus Section 4 Sullivan PreCalculus Section 4.8 Exponential Growth and Decay; Newton’s Law; Logistic Models Objectives of this Section Find Equations of Populations That Obey the Law of Uninhibited Growth Find Equations of Populations That Obey the Law of Decay Use Newton’s Law of Cooling Use Logistic Growth Models

Many natural phenomena have been found to follow the law that an amount A varies with time t according to the function: If k > 0, there is uninhibited growth. If k < 0, there is decay. A(0) = A0 represents the original amount

The half-life of Uranium-234 is 200,000 years The half-life of Uranium-234 is 200,000 years. If 50 grams of Uranium-234 are present now, how much will be present in 1000 years. NOTE: The half-life of is the time required for half of radioactive substance to decay.

( ) u t T e k = + - < Newton’s Law of Cooling kt = + - < T : Temperature of surrounding medium uo : Initial temperature of object k : A negative constant

A cup of hot chocolate is 100 degrees Celsius A cup of hot chocolate is 100 degrees Celsius. It is allowed to cool in a room whose air temperature is 22 degrees Celsius. If the temperature of the hot chocolate is 85 degrees Celsius after 4 minutes, when will its temperature be 60 degrees Celsius?

Logistic Growth Model where a, b, and c are constants with c > 0 and b > 0. The constant c is called the carrying capacity.

What is the carrying capacity? Graph the function using a graphing utility.

What was the initial amount of bacteria?

When will the amount of bacteria be 300 grams?