Warm-up #1 Describe the transformations that would be made to y = 3x. Stretch 2, Right 5, Up 1 Reflect across x-axis, Shrink 1/3, down 4

Warm-up #2 The swans on Elsworth Pond have been increasing in number each year. Felix has been keeping track and so far he has counted 2, 4, 7, 17, and 33 swans each year for the past five years. Make a scatter plot of the data. Is this a linear or exponential model? How many swans should Felix expect next year? Exponential 64

Review Homework

Skills Check

GSE Algebra I UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems? Standard: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5 Today’s Question: How is interest earned in the bank modeled with an exponential equation? Standard: MMCC9-12.F.LE.1

Exponential Growth or Decay

Growth or Decay b>1 0<b<1

Growth Or Decay?

Exponential Models y = balance P = initial t = time in years r = % of increase 1+r = growth factor y = balance P = initial t = time in years r = % of decrease 1-r = decay factor

In 2000, the cost of tuition at a state university was $4300 In 2000, the cost of tuition at a state university was $4300. During the next 8 years, the tuition rose 4% each year. Write a model the gives the tuition y (in dollars) t years after 2000. What is the growth factor? How much would it cost to attend college in 2010? In 2015? How long it will take for tuition to reach $9000? y = 4300(1 + .04)t 1.04 f(10) = 6365.05 f(15) = 7744.06 19 years, 2019, $9059.45

A 2010 Honda Accord depreciates at a rate of 11% per year A 2010 Honda Accord depreciates at a rate of 11% per year. The car was bought for $25,000. Write a model the gives the value of the car y (in dollars) t years after 2010. What is the decay factor? How much is the car worth now? In 2015? How long will it take for my car to be worth half? y = 25,000(1 – .11)t .89 f(4) = 15,685.56 f(5) = 13,960.15 6 years, 2016, $12,424

Finance Application Write a compound interest function to model each situation. Then find the balance after the given number of years. $1000 invested at a rate of 3% compounded quarterly for 5 years.

Finance Application Write a compound interest function to model each situation. Then find the balance after the given number of years. $18,000 invested at a rate of 4.5% compounded annually for 6 years.

Extension What “r” value would be used if the principal is being doubled every year? What about if it is tripled every year? 1 2

Suppose you start work at $600 a week Suppose you start work at $600 a week. After a year, you are given two choices for getting a raise: Opt. 1: 2% per week Opt. 2: a flat $15 a week raise for each successive year. Which option is better? y = 600(1 + .02)t y = 15x + 600 Option 1 gets you more money

Option A has a greater ROC from [3, 6]. Which option has the greatest ROC from [3, 6]? Option A An investment of $1,000 earns interest at a rate of 3.75%, compounded monthly. Option B y = 1000(1.0375)t Option A has a greater ROC from [3, 6].

Practice Worksheet 5 problems Classwork Practice Worksheet 5 problems

Homework Worksheet 7 problems