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4.2 Exponential Decay Functions Retesting Opportunity: Dec. 1 4.1-4.2 Quiz: Dec. 3 Performance Exam: Dec. 4.

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Presentation on theme: "4.2 Exponential Decay Functions Retesting Opportunity: Dec. 1 4.1-4.2 Quiz: Dec. 3 Performance Exam: Dec. 4."— Presentation transcript:

1 4.2 Exponential Decay Functions Retesting Opportunity: Dec. 1 4.1-4.2 Quiz: Dec. 3 Performance Exam: Dec. 4

2 Vocabulary  An exponential decay function has the form y = ab x, where a > 0 and 0 < b < 1.  The base b of an exponential function is called the decay factor.  The time required for a substance to fall to half its initial value is called half-life.

3 Example 1:  Graph y = (1/2) x

4 Example 2:  Graph y = -3(2/5) x

5 Example 3:  Graph y = 3(1/2) x+1 – 2

6 Vocabulary  Exponential Decay Model The amount y of the quantity after t years can be modeled by the equation y = a(1 – r) t, where a is the initial amount and r is the percent decrease expressed as a decimal.  Note that the quantity 1 – r is the decay factor.

7 Example 4:  The rate at which caffeine is eliminated from the bloodstream is about 15% per hour. An adult drinks a caffeinated soda, and the caffeine in his or her bloodstream reaches a peak level of 30 milligrams. Predict the amount, to the nearest tenth of a milligram, of caffeine remaining 1 hour after peak and 4 hours after the peak level.

8 Solution:  In growth to obtain the growth factor we added our rate, so exponential decay we _________ the rate of decay from 100%.  What is our decay factor?  Write the expression for the caffeine level x hours after the peak level. 30(.85) x 85% or 0.85

9 Solution continued:  What is the amount of caffeine remaining after 1 hour? 25.5 milligrams  After 4 hours? 15.7 milligrams

10 Homework:  P. 137 #1-11odd  P. 138 #10


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