HOMEWORK CHECK Take out your homework and stamp

HOMEWORK CHECK • Take out your homework and stamp page. While I am stamping homework, compare answers with your team.

CORE: QUADRATICS – WORK AS A TEAM. EVERYONE TURNS IN A PAPER. I WILL CHOOSE ONE PAPER TO GRADE! • Solve each quadratic using the indicated method. Show work when necessary. 1. 2 x 2 – 162 = 0 (by solving for x 2 and taking the square root) 2. -3 x 2 – 5 x + 9 = 0 (by graphing) 3. X 2 + 4 x – 60 = 0 (by factoring) 4. 9 x 2 – 31 x – 51 = 0 (using the quadratic formula)

DAY 3: WORD PROBLEMS UNIT 6 - EXPONENTIALS

WARM UP ZOMBIES! A rabid pack of zombies is growing exponentially! After an hour, the original zombie infected 5 people. Now those 5 zombies went on to infect 5 more people each! After a zombie bite, it takes an hour to become infected. Develop a plan to determine how many newly infected zombies will be created after 4 hours. If possible, draw a diagram, create a table, a graph, and an equation.

TODAY’S OBJECTIVES Students will explore how exponential functions can model real-world (or sci-fi) problems and solutions?

REVIEW OF VOCAB • Exponential Functions: Functions in which the variable (x) appears in the exponent. f(x) = a • bx • Initial Value: The amount you start with. Represented by “a” in the function or the y-intercept on a graph, occurs when x = 0. • Growth/Decay Factor: The rate at which the values increase or decrease, represented by “b” in the function. • If b > 1, then the function is growing. • If 0 < b < 1, then the function is decaying.

BACK TO ZOMBIE PROBLEM • What was the initial value, a, from the warm up question? • a=1 zombie • What was the growth/decay factor, b? • b=5 because the number of zombies increased by a factor of 5 each time. • What function represents this model? • f(x) = 1 • 5 x, where x is hours since first zombie

KNIGHTDALE APOCALYPSE! • Use your graphing calculator to determine the time when all of Knightdale has been infected. That is, when 12, 724 people are infected. 12, 724 = 1(5)x x= 5. 87 hours…. . scary….

WORD PROBLEM EXAMPLE 1 • In a laboratory, one strain of bacteria can double in number every 15 minutes. • Suppose a culture starts with 60 cells. Use your graphing calculator or a table of values to show the sample’s growth after 2 hours. • This can be modeled by the equation y = 60(2)x, where x is sets of 15 minutes. • How many sets of 15 minutes happened in 2 hours? • 8 sets of 15 minutes • Plug in x and solve y = 60(2)8 • 15, 360

WORD PROBLEM EXAMPLE 2 • The typical car loses 15 -20% of its value each year. The graph below shows the value of a car that is depreciating 20% each year.

WORD PROBLEM EXAMPLE 2 1. What was the value of the car when it was new? 2. When did the car lose the most value?

WORD PROBLEM EXAMPLE 3 • You are investing $10, 000 at 6% interest, compounded annually. Use y = 10, 000(1. 06)t. • How long will it take for there to be $25, 000 in the account? Round to nearest year.

WORD PROBLEM EXAMPLE 4 • How long will it take for an investment of $15, 000 at 5% interest compounded annually to triple? • Use y = 15000(1. 05)t. Round to nearest year.

WORD PROBLEM EXAMPLE 5 • Suppose that you are given a choice of investing $10, 000 at a rate of 7% y = 10, 000 (1. 07)t OR $5, 000 at a rate of 12% y = 5, 000 (1. 12)t When will the investments be worth the same? If the money will be yours when you are 50, which investment plan should you choose?

EXTENSION: DICE GAME • Everyone needs to stand so that the recorder can count everyone and record the number of people standing. • Use your random number generator to “roll the dice” • If you roll a 1, sit down. Otherwise remain standing so the recorder can count the number of people standing. • We will continue until less than 3 people are standing.

DICE GAME • What was our initial value? • Was this growth or decay? • Decay • What was the decay factor? • (5/6) because only 1/6 sides of the dice made you sit down so 5/6 could stay standing • Write an equation to represent this model.

HOMEWORK • Problems 1 and 2 on page 30