Lesson 5.1: Exponential Growth and Decay. General Form of an Exponential Function y = ab x The total amount after x periods The initial amount The growth/decay.

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Presentation transcript:

Lesson 5.1: Exponential Growth and Decay

General Form of an Exponential Function y = ab x The total amount after x periods The initial amount The growth/decay factor The number of periods

When b>1 The growth factor = b – 1 (turn the decimal into a %) When 0<b<1 The decay factor = 1 – b (turn the decimal into a %)

Example #1 The United States population since 1960 can be modeled by the function y = 180(1.011) x, where x is the number of years since 1960 and y is the populatio in millions. x represents_______________________ y represents_______________________ What is the growth factor? What is the percentage rate of growth per year? What was the population of the United States in 1960? What was the population during the year you were born? 2010?

Example #2 As technology advances, the price of many technological devices such as scientific calculators and camcorders goes down. Suppose y = 89(0.94) x represents the cost of a certain calculator since x represents________________________ y represents________________________ What is the decay factor? What is the percentage rate of decay per year? What was the cost of the calculator in 2005? What would the cost be today?

Example #6 The presence of medicine for reducing high blood pressure decreases at the rate of 29% per hour in a patient’s bloodstream. This medicine is effective until the amount in the bloodstream drops below 1.2mg. How long will a dose of 75mg be effective?