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Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
1
March 16, 2016
DO NOWRegina 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!
After ten days, how many people will be told 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.
Algebra I 03/18/16Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
2
March 16, 2016
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
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!
After ten days, how many people will be told the rumor Regina started? 59,049 People
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
3
March 16, 2016
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?
Question: What is different about this situation?Discuss with your partner
Exponential Decay
starting amount
y = a bxThe base, or decay factor,is between 0 and 1
exponent, usually # years
amount after time
Exponential decay can be modeled with the same function as exponential growth, but the growth factor, b, is between 0 and 1
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
4
March 16, 2016
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Real World Examples of Exponential Functions/Decay
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
5
March 16, 2016
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?
starting amount
y = a bxThe base, or decay factor,is between 0 and 1
exponent, usually # years
amount after time
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
6
March 16, 2016
Exponential Decay ~ Depreciation
As a Class?
With Partner?
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?
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
7
March 16, 2016
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
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?
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
8
March 16, 2016
How do we find the base for an exponential decay function that involves percentage?
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
9
March 16, 2016
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 notsogreat neighborhood for $226,000 has lost 4% of its value each year for the past five years. What is it worth now?
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
10
March 16, 2016
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 notsogreat neighborhood for $226,000 has lost 4% of its value each year for the past five years. What is it worth now?
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
11
March 16, 2016
1) The function y = 25 * 0.80x models the amount y of a 25mg 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?
Exit SlipREGENTS PREP
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
12
March 16, 2016
1) The function y = 25 * 0.80x models the amount y of a 25mg 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?
Exit SlipREGENTS PREP
Aim: How Do We Model Situations Involving Exponential Decay?HW#77: Exponential Functions Day 3 WS
Algebra 1 of 4 Unit 4 Day 3 Exponential Functions Day 3.notebook
13
March 16, 2016
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