Exponential Functions and Their Graphs Ch 3.1 Exponential Functions and Their Graphs So far in this course, you have been investigating the family of linear and quadratic functions using multiple representations (especially tables, graphs, and equations).  In this chapter, you will learn about a new family of functions and the type of growth it models

Hw for after Ch 2 Test

*10 min

Get out your PT and I will check it off. Start… Exponential Equation Warm Up #1 MULTIPLYING LIKE BUNNIES In the book Of Mice and Men by John Steinbeck, two good friends named Lenny and George dream of raising rabbits and living off the land.  What if their dream came true? Suppose Lenny and George started with two rabbits and that in each month following those rabbits have two babies.  Also suppose that every month thereafter, each pair of rabbits has two babies. Month # of bunnies 1 2 4 3 8 16 5 32 6 64 7 128 Month # of bunnies 1 2 3 4 5 6 7 Draw a diagram to represent how the total number of rabbits is growing each month. How many rabbits will Lenny and George have after three months? 2) As the number of rabbits becomes larger, a diagram becomes too cumbersome to be useful.  A table might work better.  Organize your information in a table showing the total number of rabbits for the first several months (at least 6 months).  What patterns can you find in your table?  Describe the pattern of growth in words. 3) Make an equation to represent the situation

Exponential Equation Warm Up #2 Each year the local country club sponsors a tennis tournament.  Play starts with 128 participants.  During each round, half of the players are eliminated.  How many players remain after 5 rounds? Make a table of values to help you solve this problem. What equation can be modeled by this situation? Round # # of players 1 128 2 3 4 5 6 Round # # of players 1 128 2 64 3 32 4 16 5 8 6 Y = 128 (1/2)^t

Exponential Functions: Applications of Exponential Functions: ”half life” and population growth 2) Radioactive Decay 3) Interest! https://www.youtube.com/watch?v=KIpcCyuypzg

What are exponential functions? The exponential function f with a base of a is denoted by f(x) = a 𝑏 𝑥−ℎ +𝑘 where b > 0, x is any real number, and b ≠ 1 Think about it: Why can “b” not be equal to 1? f(x) = 𝑏 −𝑥 f(x) = 𝑏 𝑥 When b > 1, the graph of f(x) = 𝑏 𝑥 is increasing over its domain When b > 1, the graph of f(x) = 𝑏 −𝑥 is decreasing over its domain When 0< b < 1 the graph of f(x) = 𝑏 𝑥 is decreasing over its domain

EX 1: Sketch the graph of f(x) = 3 −𝑥 Then sketch f(x) = 3 −𝑥 +2 Step 1: Make a table centered around the starting value h Step 2: Plot these values and sketch your graph

You Try! Sketch the graph of f(x) = 4 𝑥−1 +2

EX 2: Exponential Applications with Radioactive Decay Let y represent a mass, in grams, of radioactive strontium, whose half life is 29 years. The quantity of strontium present after t years is What is the initial mass when t = 0? How much of the initial mass is present after 80 years?

What is the Natural Base e? The natural exponential function is denoted by f(x) = 𝑒 𝑥 Where e = ________ Treat it like you treat the irrational number π 2.71

Application #3….MONEY!

Talk about the following questions in your groups… Would a customer not paying off his/her debt be profitable for the credit card company ? What is "interest?" How does it work? Is it possible to use a credit card without having to pay any interest or fees? What are some ways customers could get in financial trouble with credit cards? Do you think credit card companies want customers to pay off their balances? -When someone makes a purchase with a credit card, he is borrowing the money. -"Interest" is what the company charges for the privilege of borrowing their money, and it's a percentage of the amount borrowed. Typically, if a customer repays the credit card company within thirty days, no interest is charged (though other fees may apply). The longer it takes to pay back, the more interest they can charge.

Compounded monthly b) compounded daily c) compounded continuously EX 3: Find the amount in an account after 10 years if $6000 is invested at an interest rate of 7% Compounded monthly b) compounded daily c) compounded continuously b) $12081.70 c) $12082.51 a)$12057.96

You Try! A total of $9000 is invested at an annual interest rate of 2.5%,. Find the balance in the account after 5 years. a) Compounded annually b) compounded continuously