Algebra I 02/03/17 Aim: How Do We Model Situations Involving Exponential Decay? HW: Exponential Functions Day 3 WS

Transcription

1 Algebra I 02/03/17 DO NOW Regina is such a gossip! She decided to start a rumor about a junior boy and told three of her friends the story she made up. The next day those three girls each told another three people about the rumor. And the next day each of those people each told another three people. This pattern went on day after day! On the day ten, how many people will hear the rumor Regina started? Hint: Determine whether or not this is a linear or exponential situation and write a rule. Create a table or draw a diagram to model the situation if you need a visual element. 1

2 Regina is such a gossip! She decided to start a rumor about a junior boy and told three of her friends the story she made up. The next day those three girls each told another three people about the rumor. And the next day each of those people each told another three people. This pattern went on day after day! On day ten, how many people will hear the rumor Regina started? 59,049 People 2

3 Question: What is different about this situation? Discuss with your partner Since 1980, the number of gallons of whole milk each person in the United States drinks each year has decreased 4.1% each year. In 1980, each person drank an average of 16.5 gallons of whole milk per year. What was the approximate consumption per person of whole milk in 2000? Exponential Decay Exponential decay can be modeled with the same function as exponential growth, but the growth factor, b, is between 0 and 1 starting amount amount after time y = a b x The base, or decay factor, is between 0 and 1 exponent, usually # years 3

4 Real World Examples of Exponential Functions/Decay 4

5 Exponential Decay ~ Depreciation A new car is worth $20,000. It depreciates in value (decreases in value) at a rate of 15% per year. What will the car be worth in five years? As a Class? With Partner? 5

6 A new car is worth $20,000. It depreciates in value (decreases in value) at a rate of 15% per year. What will the car be worth in five years? 6

7 How do we find the base for an exponential decay function that involves percentage? 7

8 1) A powerful computer is purchased for $2000, but on the average loses 20% of its value each year. How much will it be worth 4 years from now? 2) A house purchased in a not so great neighborhood for $226,000 has lost 4% of its value each year for the past five years. What is it worth now? 8

9 1) A powerful computer is purchased for $2000, but on the average loses 20% of its value each year. How much will it be worth 4 years from now? 2) A house purchased in a not so great neighborhood for $226,000 has lost 4% of its value each year for the past five years. What is it worth now? 9

10 REGENTS PREP Exit Slip The function y = 25 * 0.80 x models the amount y of a 25 mg dose of medicine remaining in the bloodstream after x hours. a) Is this function an example of exponential growth or decay? b) How many milligrams of medicine remain in the bloodstream after 5 hours? 10

11 REGENTS PREP Exit Slip 1) The function y = 25 * 0.80 x models the amount y of a 25 mg dose of medicine remaining in the bloodstream after x hours. a) Is this function an example of exponential growth or decay? b) How many milligrams of medicine remain in the bloodstream after 5 hours? 11

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