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

2. Vocabulary
An exponential decay function has the form y = abx, 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