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. 2x2 – 162 = 0 (by solving for x2 and taking the square root)

2. -3x2 – 5x + 9 = 0 (by graphing)3. X2 + 4x – 60 = 0 (by factoring)4. 9x2 – 31x – 51 = 0 (using the quadratic formula)

U N I T 6 - E X P O N E N T I A L S

DAY 3: WORD PROBLEMS

WARM UPZOMBIES!

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•5x, 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 has 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