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

2. 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. 1.2x 2 – 162 = 0 (by solving for x 2 and taking the square root) 2.-3x 2 – 5x + 9 = 0 (by graphing) 3.X 2 + 4x – 60 = 0 (by factoring) 4.9x 2 – 31x – 51 = 0 (using the quadratic formula)

3. UNIT 6 - EXPONENTIALS DAY 3: WORD PROBLEMS

4. 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.

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

6. REVIEW OF VOCAB Exponential Functions: Functions in which the variable (x) appears in the exponent. f(x) = ab x 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.

7. 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) = 15 x, where x is hours since first zombie

8. 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….

9. 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 has happened in 2 hours? 8 sets of 15 minutes Plug in x and solve y = 60(2) 8 15,360

10. 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.

11. 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?

12. 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.

13. 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.

14. 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?

15. 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.

16. 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.

17. HOMEWORK Problems 1 and 2 on page 30