Chapter 4 Sec 7 Inverse Matrices

2 of 17 Algebra 2 Chapter 10 Sections 1 Finding Inverses (step by step) Step 1 - Find the Determinate (ad – bc) Does the Det = 0? Yes ? Then No Inverse Exists No ? Step 2: Step 3: Distribute the

3 of 17 Algebra 2 Chapter 10 Sections 1 Finding the Inverse Find the inverse of each matrix, if it exists. Find the value of the determinant Since the determinant equals 0, R -1 does not exist.

4 of 17 Algebra 2 Chapter 10 Sections 1 Finding the Inverse Find the inverse of each matrix, if it exists. Find the value of the determinant Since the determinant does not equal 0, P -1 does exist.

5 of 17 Algebra 2 Chapter 10 Sections 1 Finding the Inverse Find the inverse of each matrix, if it exists.

6 of 17 Algebra 2 Chapter 10 Sections 1 Verifying Inverses Determine whether each pair of matrices are inverses. Take one matrix and find the inverse, then compare to the other. If they equal then Yes they are inverses if not NO. P -1 = Q So they are inverses

Chapter 10 Sec 1 Exponential Functions

8 of 17 Algebra 2 Chapter 10 Sections 1 Power of 2 Which would desire most. 1.$1, 000, 000 in 30 days or… 2. 2 cents today then doubled for 30 days.

9 of 17 Algebra 2 Chapter 10 Sections 1 Power of = = = 20, = = = 41, = = = 83, = = = 167, = = = 335, = = = 671, = = 1, = 1,342, = = 2, = 2,684, = = 5, = 5,368, = = 10, = 10,737,418.24

10 of 17 Algebra 2 Chapter 10 Sections 1 Exponential Function From the previous example we can see, to find the amount of money accumulated, y, over x amount of days can be written as: y = 2 x. This type of function, in which the variable is the exponent, is called an exponential function.

11 of 17 Algebra 2 Chapter 10 Sections 1 Graph an Exponential Function a. Graph y = 2 x. x 2x2x2x2xy / /

12 of 17 Algebra 2 Chapter 10 Sections 1 Graph an Exponential Function x 1/2 x y -3 1/ / / / /2 1 1/2 21/2 2 1/

13 of 17 Algebra 2 Chapter 10 Sections 1 Exponential Functions In general, an equation of the form, y = ab x, where a = 0, b > 0, and b = 1, is called and exponential function with base b. There are two types of exponential functions: exponential growth and exponential decay. The base of an exponential growth is a number greater than 1. The base of an exponential decay is a number between 0 and 1.

14 of 17 Algebra 2 Chapter 10 Sections 1 Exponential Functions In general, an equation of the form, y = ab x, where a = 0, b > 0, and b = 1, is called and exponential function with base b.

15 of 17 Algebra 2 Chapter 10 Sections 1 Identify Exponential Growth and Decay Determine whether each function represents exponential growth or decay. Function Exponential Growth or Decay? The function represents exponential decay, since the base, 1/5 is between 0 and 1. The function represents exponential growth, since the base, 4 is greater than 1. The function represents exponential growth, since the base, 1.2 is greater than 1.

16 of 17 Algebra 2 Chapter 10 Sections 1 Solve Exponential Growth/Decay The number of bacteria in a colony is growing exponentially. a.Write an exponential function to model the population y of the bacteria x days after day 1. (find a and b) Log Day Number of bacteria ,200 Day 4: x = 4 – 1 = 3

17 of 17 Algebra 2 Chapter 10 Sections 1 Solve Exponential Growth/Decay The number of bacteria in a colony is growing exponentially. b. How many bacteria were there at day 5. Log Day Number of bacteria ,200 Day 5: x = 5 – 1 = 4

18 of 17 Algebra 2 Chapter 10 Sections 1 Daily Assignment Study Guide (SG) Pg 129 All Text book Pg 529 # 57 – 61 Pg 836 Lesson 4.7 #1 – 16 All

19 of 17 Algebra 2 Chapter 10 Sections 1 Solve Exponential Growth/Decay The number of bacteria in a colony is growing exponentially. a.Write an exponential function to model the population y of the bacteria x hours. (Find a and b) (Find a and b) Log Time Number of bacteria 3 am am 1,600 Time x = 6 – 3 = 3

20 of 17 Algebra 2 Chapter 10 Sections 1 Solve Exponential Growth/Decay The number of bacteria in a colony is growing exponentially. b. How many bacteria were there at 9 am. Log Time Number of bacteria 3 am am 1,600 Time: x = 9 – 3 = 6