Honors Algebra 2



Honors Algebra 2

Quarter 4 Project

Centers for

Cubic Polynomials

& Exponentials

Due Dates:

A Day: May 7, 2013

B Day: May 8, 2013

Group Members:

_____________________

_____________________

_____________________

Center #7

Finding the Final Amount

1. The price of school lunch increases 15% annually. If the current price is $2.50, what will be the price in 5 years?

2. A car depreciates 12% annually. If you bought a car new for $16,500, what will be its value in 7 years?

3. Suppose you invest $500 at [pic]% apr* that is compounded monthly. What is your balance at the end of 5 years?

4. James purchased a truck for $25,900. The value of the truck decreases by 12% per year. What will be the approximate value 8 years after the purchase?

*apr stands for Annual Percentage Rate

Center #8

Finding the Rate

1. Chandler bought a boat 3 years ago for $5550. Today the same boat sells for $7189. What is the rate of appreciation?

2. A car purchased 2 years ago for $12,900 is now worth $8975. What is the rate of depreciation?

3. The Banks family bought a new house three years ago for $92,000. The house is now worth about $113,000. Assuming a steady annual growth rate, approximately what was the yearly rate of appreciation?

Center #9

Finding the Time

1. An exponential growth formula is [pic], where:

N is the population at time t,

N0 is the initial population,

k is the growth rate, and

t is the time in years

The enrollment of a school has been increasing exponentially at a rate of 1.5% per year. The school’s enrollment now is 1,800. Approximately how long ago was the school’s enrollment 1,200.

2. Karra invested $500 at 6% annual interest compounded quarterly. Exactly how long will it take for her investment to be worth four times as much in value?

3. If the price of theater tickets increases 8% annually, how long will it take the current price to double? (Hint: Pick an initial price, any price, and double it!)

4. If the price of shoes increases at a rate of 11% annually, how long will it take the current price to triple? (Hint: Pick an initial price, any price, and triple it!)

Center #10

Finding the Amount of Interest Earned

1. Suppose you invest $150 at 4% apr. Find your balance at the end of 3 years. How much interest have you earned?

2. Suppose you invest $1500 at 4% apr but it is compounded quarterly. Find your balance at the end of 3 years. How much interest have you earned?

3. If you deposit $500 into a bank account earning [pic] annual percentage rate, how much interest is earned in 10 years if you make NO withdrawals or deposits?

4. Suppose you invest $1000 at [pic] apr compounded quarterly. How much interest do you earn in 4 years?

*apr stands for Annual Percentage Rate

Center #11

Exponential Data and Modeling

1. The table below shows the value of an investment fund.

|Time, t (years) |3 |5 |7 |9 |11 |13 |15 |

|Value of Fund |$15, 700 |$18, 400 |$21, 400 |$25,000 |$29,100 |$34, 200 |$39,700 |

a) Find the exponential function that models this data. (STAT CALC 0)

b) According to the table, after how many years will the value of the fund be $50,000?

2. The table below shows the total sales for a new product during the first five years of production.

|Year |1 |2 |3 |4 |5 |

|Sales (Thousand of $) |2 |6 |11 |29 |68 |

a) Find the exponential model for the data.

b) According to the best-fit exponential model, what was the approximate annual rate of growth in sales during this period? (Look at the b value of your function).

3. The table shows the growth of a certain bacteria.

|Time in hours, x |0 |1 |2 |3 |4 |5 |

|Number of Cells, N|50 |71 |100 |141 |200 |283 |

If N represents the number of cells at time x, find the equation which best models this set of data.

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Center #3 - Factoring Polynomials

In this center, you will break down a cubic function to its factors.

1. Given x – 3 is a factor, find the other factors of

2x3 – 7x2 - 12x + 45

2. Is x – 2 a factor of f (x) = x3 – 5x2 – x + 6? Why or why not?

3. Find the dimensions of the rectangular prism given the volume is 4x3 – 12x2 – x + 3 and the length is x – 3.

?

?

x – 3

Center #1 - Operation of Functions

and Inverses

Given f (x) = x + 4 and g (x) = x2 + 4x – 6, complete the following:

1. g (–3)

2. f (x) – g (x)

3. f (x) · g (x)

4. g (f (x))

5. Given [pic], find f -1 (x).

Center #2 - Dividing Polynomials

In this center, you will divide different types of

polynomials. You may use synthetic division or

simplification by reducing.

Divide:

1. [pic]

2. (y3 + 3y2 – 5y – 4) ÷ (y + 4)

3. [pic]

4. (6y3 - 3y2 - 15y - 6) ÷ (6y + 3)

**Remember to divide answer (except remainder) by 6**

Center #6 - Applications of Cubic Functions

An employee at Kellogg’s cereal company is designing a box from a rectangular sheet of cardboard that measures 40 inches by 25 inches. She designs the box by cutting congruent squares away from each of the four corners and turns up the sides.

1. Write the equation to model the volume of the box.

2. What is the maximum amount of cereal the box can hold?

3. What are the dimensions of the box that will hold this maximum volume? (Give length, width, and height!)

4. Suppose the box must hold exactly 1500 in3 of cereal. What is the value for x that will create this box?

5. In #4, what would be the better choice for creating the box that will hold 1500 in3? Explain.

Center #5 - Finding Zeros

In this center, you will find all the zeros of a polynomial. Remember these steps:

1. Find as many roots as possible using your calculator.

2. If you find only one root in the calculator, use

synthetic division with your root.

3. Use the quadratic formula to solve.

4. List all roots in your final answer

(number of solutions is equal to the degree).

1. Find all the zeros of x3 – 2x2 - 10x + 21.

2. Find all the zeros of f (x) = x3 - 6x2 + x + 34.

3. Given the roots –2, 1, 3, work backwards to find the function with these roots.

4. Find the function with the given roots: 4, 3 + i.

x – 3

Center #4 - Graphing Polynomials

In this center, you will make decisions about what the graph of a specific polynomial looks like.

1. Give an example of a cubic function whose left behavior goes down and right behavior goes up.

2. Give an example of a cubic function whose left behavior goes up and right behavior goes down.

3. True or False: A cubic function can have 2 real roots and 1 imaginary root. Give an explanation for your answer.

4. For the graph below, fill in the blanks with the correct information:

A. There are _____ x-intercepts.

B. The roots of this polynomial are x = {________}.

C. The end behavior is _____ on the left and ____ on the right.

D. This polynomial must have at least a degree of____.

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