) 2 ( 2x 3 y 5 12x 9 y 12

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1 (A) Lesson Context BIG PICTURE of this UNIT: Do mathematical operations transfer to polnomials? How can we appl polnomials to area and perimeter? Where we ve been Where we are Where we are heading CONTEXT of this LESSON: Working with linear functions and polnomials. Exploring exponent laws and exponential equations. Being able to distinguish between different tpes of exponential b looking at data, graphs, etc. (B) (C) Lesson Objectives: a. Practice product, quotient, and power rule for exponents. b. Review negative and zero exponent rules. c. Comparing Exponential equations and graphs. Warm-up Simplif the following: ( ) 7 ( x 6 ) 11 x 3 5 ( x 2 3 ) 4 x 5 8 ( 2x 6 9 ) 2 ( 2x 3 5 ) 3 12x 9 12

2 (D) Exponent Rules Exploration Negative and Zero Exponents Continue the pattern in the tables below: What do ou notice? What do ou notice about 2 0 and 3 0? Based on our observations, predict a rule for an base to the zero. x 0 = What do ou relationship do ou notice between 2 2 and 2 2? 3 3 and 3 3? 2 4 and 2 4? Based on our observations, predict a rule a base to a negative exponent. x n =

3 (E) Comparing Exponential Equations 1. Use the following Desmos link to investigate the graphs of exponential equations in the form = a( b) x Pla with the sliders and make some observations: i. When b > 1, describe what is happening to the graph. ii. When 0 < n < 1, describe what is happening to the graph. iii. What does a/m affect on the graph? (F) Predictions of Exponential Equations For each of the following equations: 1. Write down the value of b. 2. Predict the shape (draw a quick sketch) 3. Create a table of values from 3 x Plot the points and then reflect on our work does the actuall graph match our predicted graph? = 2( 3) = 4 (.1) x = 8 1 x 2 = 1 2 ( 4)x = 9 (.3) x = 4( 2)

4 (G) Exponential Growth & Deca Applications (from MathBitsNotebook.com) Example 1: A common example of exponential growth deals with the growth of bacteria. Bacteria have the abilit to multipl at an alarming rate, where each bacterium splits into two new cells, doubling the number of bacteria present. Let's start with one bacterium, which can double ever hour. a. Make a table showing the number of bacteria present from 0 to 10 hours. c. What is the equation for the number of bacteria present in the form = a( b) x (a=initial amount; b=growth/deca factor) d. How man bacteria will be present after 8 hours? Example 2: The NCAA Basketball Championship (also known as March Madness) is an example of exponential deca. At each round of the tournament, teams pla against one another with onl the winning teams progressing to the next round. In other words, the number of teams plaing at each round is half of the number of teams plaing in the previous round. Let's start with 64 teams going into round 1. How man teams are left to begin pla in round 5? a. Make a table showing the number of teams left from 0 to 6 rounds. c. What is the equation for the number teams left in the form = a( b) x (a=initial amount; b=growth/deca factor) d. How man teams are left to begin pla in round 5?

5 (H) Exponential Growth & Deca Applications examples from last class 1. Marissa has saved $1000 in a jar. She plans to withdraw half of what s remaining in the jar at the end of each month. a. Make a table showing the amount of mone left in the jar from 0 to 12 months. c. What is the equation for the amount of mone left in the jar in the form = a( b) x (a=initial amount; b=growth/deca factor) d. How much does Marissa have left in the jar at the end of 8 months? 2. The volume of a landfill starts at 1 cubic meter and the volume doubles ever three ears. a. Make a table showing the amount of volume of the landfill from 0 to 9 ears. c. What is the equation for the volume of the landfill in the form = a b b=growth/deca factor) d. What is the volume of the landfill after 7 ears? ( ) x (a=initial amount;