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Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
1
February 02, 2017
DO NOW
Algebra I 02/02/17Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Using complete sentences, explain your answer choice.
REGENTS PREP
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
2
February 02, 2017
Using complete sentences, explain your answer choice.
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
3
February 02, 2017
Real World Examples of Exponential Functions/Growth
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
4
February 02, 2017
Retire a Millionaire?!?If you invest $1000 this year, and earn 5% interest each year, how much money will you have after one year? Two years?
Six years? Sixty years?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
5
February 02, 2017
If you invest $1000 this year, and earn 5% interest each year, how much money will you have after one year? Two years?
Six years? Sixty years?
The LOOOOOOOOOOOOOOOOONG way
year 0
year 1
year 2
year 3
year 4
year 5
year 6
1, 000
1000 + 1000 (. 05)1, 0001, 050
1050 + 1050 (.05) 1, 102.50
1102.5 + 1102.5 (.05) 1, 157.63
1157.63 + 1157.63 (.05) 1, 215.51
1, 276.281000 * (1.05)5
1000 * (1.05)6 1, 340.10
year 60 1000 * (1.05)60 18, 679.19
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
6
February 02, 2017
Exponential Growth
starting amount
y = a bx
Exponential growth can be modeled with the function:
The base, or growth factor,is always greater than 1 for exponential growth.
exponent, usually # years
amount after time
If you invest $1000 this year, and earn 5% interest each year, how much money will you have after one year? Two years?
Six years? Sixty years?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
7
February 02, 2017
Exponential Growth ~ Money
You invested $475 in an account that earns an 8.5% interest rate. How much money will you have at the end of 12 years?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
8
February 02, 2017
Exponential Growth ~ PopulationIn 2000, Florida's population was about 16 million. Since 2000, the state's population has grown about 2% each year. Find Florida's population in 2007.
As a Class?
With Partner?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
9
February 02, 2017
Exponential Growth ~ Population In 2000, Florida's population was about 16 million. Since 2000, the state's population has grown about 2% each year. Find Florida's population in 2007.
y = 16,000,000(1.02)7102% as a decimal (growth factor)
number of years since
2000
Formula y = a bx Use an exponential function
Define Let a = the initial (starting) population, variables Let b = the growth factor, which is 100% + 2% =
102% = written as a decimalLet x = the number of years since 2000, Let y = the current population
Substitute
Solve use a calculator
Florida's population in 2007 was about
18,378,971 people
starting amount
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
10
February 02, 2017
How do we find the base for an exponential growth function that involves percentage?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
11
February 02, 2017
2) Suppose your parents deposited $1500 in an account earning 3.5% interest compounded annually (once a year) when you were born. Find the account balance after 18 years.
1) A species of rare, deep water fish has an extremely long lifespan and rarely have reproduce. If there are a total of 821 of this type of fish and their growth rate is 2% each month, how many will there be in half of a year?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS
Algebra Unit 5 Day 2 Exponential Functions Day 2.notebook
12
February 02, 2017
2) Suppose your parents deposited $1500 in an account earning 3.5% interest compounded annually (once a year) when you were born. Find the account balance after 18 years.
1) A species of rare, deep water fish has an extremely long lifespan and rarely have reproduce. If there are a total of 821 of this type of fish and their growth rate is 2% each month, how many will there be in half of a year?
Aim: How Do We Model Situations Involving Exponential Growth?HW: Exponential Functions Day 2 WS