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Unit 8: Exponential Functions
x-8.1:‍x-7.1:‍8.1:‍8.1:
In your online journal:
Identify each variable in an exponential growth model and say what it represents.
Given the scenario below, use the equation to find p(2) and explain in complete sentences what you have just determined in the context of the situation.
The population of Jacksonville was 3,810 in 2007, and is growing at an annual rate of 3.5%. The population of Jacksonville can be modeled by the function P(t) = 3810(1.035)^t.
3,810 is the initial amount
2007(0) is the time exponent
3.5 anual rate - 0.035
Base is > than 1 its exponential growth
Base is < than 1 its exponential decay
P(2) : 4081.36 is the population in the year 2009
x-8.2:‍8.2:
Look at the graph below. Both exponential growth models represent two different bank accounts.

Would you choose that same account to start your child's college fund (if you had a child) and why?
1. 1000(1+.0599)^t
and for both equationsBlue is (0,10500) and Red (0,1000)
3.The red account is better but this is not always true because when the x value is 0 the y value is only 1000. However, in the blue account when x is 0 y is 10500 which is $500 more than the original amount was $1000.in the red account.
4. The Red account because it is better long term.
5. Yes, I would because it is much more benificial long term.

Which account would you choose when opening to save up for your college in a few years and why?
Would you choose that same account to start your child's college fund (if you had a child) and why?
1. 1000(1+.0599)^t
2. The y-intercept is the initial amount and for both equations the original amount was $1000.

Unit 8: Exponential Functions
x-8.1:‍x-7.1:‍8.1:
In your online journal:
Identify each variable in an exponential growth model and say what it represents.
Only looking at an equation, how would you determine if the function represents a growth model or a decay model?
Also, copy the equation into your notebook for class and have each variable labeled to be ready for class.
Given the scenario below, use the equation to find p(2) and explain in complete sentences what you have just determined in the context of the situation.
The population of Jacksonville was 3,810 in 2007, and is growing at an annual rate of 3.5%. The population of Jacksonville can be modeled by the function P(t) = 3810(1.035)^t.
x-8.2:‍8.2:
Look at the graph below. Both exponential growth models represent two different bank accounts.
The blue exponential growth model represents a bank account where a person deposited $1000 with a $50 bonus for signing up. The account has a 4.99% interest rate and the interest is compounded annually.
The red exponential growth model represents a bank account where a person deposited $1000. The account has a 5.99% interest rate and the interest is compounded monthly.
{chapter_8_bank_accounts.jpg} chapter_8_bank_accounts.jpg
Compare and contrast the two bank accounts in your online journal by answering the following questions:
Write a function that represents the red exponential growth model.
What is the y-intercept of each function? Explain in the context of the situation.
Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
Which account would you choose when opening to save up for your college in a few years and why?
Would you choose that same account to start your child's college fund (if you had a child) and why?

6.1:
For each of the groups below, identify the graph that does not belong and state your reasoning why that graph does not belong in your online journal.
{group_1_chapter_6.jpg} group_1_chapter_6.jpg
{group_2_chapter_6.jpg} group_2_chapter_6.jpg
{Group_3_chapter_6.jpg} Group_3_chapter_6.jpg
{group_4_(2)_chapter_6.jpg} group_4_(2)_chapter_6.jpg
Group One: The first graph does not belong because that equation is a linear equation due to its exponent being only one.
Group Two: Again, graph two doe not belong because it is a linear equation since its highest exponent is to the power of one.
Group Three: Graph three is also a linear equation.
Group Four: Graph three is a linear function.
x-6.2:6.2:
Summarize the last two days of class in your online journal. We have discussed different methods for graphing polynomial functions in intercept form. In detail, explain the graphing method to a student who has missed the last two days.
Whenever graphing polynomials one needs to find the x-intercepts by having the parenthesis equal to 0. Finding the y-intercept is the next process where one just plugs 0 in for the variable x. The degree and the leading coefficient are the last two things. It tells one the end behavior allowing the completion of the graph.

5.1: List5.1:List the following
quadratic - highest exponent is 2
vertex - Highest point
5.2: Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function.
Differences:
graph; a parabola.parabola
5.5:
You and your friend are playing a game of tennis. Your friend throws the ball in the air, hitting the ball when it is 3 ft above the court with an initial velocity of 40 ft/sec. The height h(t) of the ball can be modeled by the function h(t) = -16t^2+40t+3, where t is the elapsed time in seconds after the dive.
Answer the following questions in your wikispace.
What shape does the path of the tennis ball make while traveling in the air.
Find h(1). Describe what h(1) means in the context of the problem
What is the y-intercept of h(t). In context, what does the y-intercept represent?
Identify the vertex. Describe in context what the x-coordinate of the vertex represents. Describe in context what the y-coordinate of the vertex represents.
What is the x-intercept(s) of h(t). In context what does the x-intercept(s) represent?
- Shape of the path is a curve.
x-5.5:--h(1)=3 which is the initial height of the tennis ball.- h (1) = 3 (initial height of the tennis ball).
x-5.5:--The y-intercept is ( 0,3) . During the 0 secs the ball was at 3ft.- The y-intercept is ( 0,3) . At 0 seconds the ball was at 3 feet.
x-5.5:--The vertex=(1.25,27.4) The x coordinate of the vertex represents the the time where the ball will reach its highest point. The y coordinate is where the ball will reach its highest point.- Vertex = (1.25, 27.4) X coordinate of the vertex represents the the time where the ball will reach its highest point. Y coordinate is where the ball will reach its highest point.
x-5.5:--The x-intercept=(2.6,0) The X-intercept represents the time of the ball dropping.- The x-intercept = (2.6, 0) X-intercept represents the time of when the ball drops.
.

5.1:
x---List the following words and give a mathematical definition in your own words on your wikispace. Remember, you may edit your definitions after we begin the unit.List List the following the unit.
x---quadratic - highest exponent is 2quadratic
quadratic - highest is 2
x---vertex - Highest pointvertex
vertex - Highest point
x---x-intercept - A point at which the line crosses the x axisx-intercept
x-intercept - The x axis
x---y-intercept - A point at which the line crosses the y axisy-intercept
y-intercept - The y axis
x---increasing -** **The y-value increases as the x-value increases.increasing
increasing - The x-value increases.
x---decreasing - The y-value decreases as the x-value increases.decreasing
decreasing - The x-value increases.
x---maximum - Highest pointmaximum
maximum - Highest point
x---minimum - Lowest pointminimum
minimum - Lowest point
x---parabola - A U-shaped graph of a quadratic equationparabola
parabola - A quadratic equation
5.2: Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function.
Differences:
linear functions describes a line i.e 3x+2=y. Graphing that equation would result in a line. An example of a quadratic equation is x^2+3x+1=y. Graphing this equation would give you a U shaped graph; a parabola.

5.1:
x---List the following words and give a mathematical definition in your own words on your wikispace. Remember, you may edit your definitions after we begin the unit.List the following words and give a mathematical definition in your own words on your wikispace. Remember, you may edit your definitions after we begin the unit.
x---quadratic - highest exponent is 2quadratic - highest exponent is 2
x---vertex - Highest pointvertex - Highest point
x---x-intercept - A point at which the line crosses the x axisx-intercept - The point where the line crosses the x axis
x---y-intercept - A point at which the line crosses the y axisy-intercept - The point where the line crosses the y axis
x---increasing -** **The y-value increases as the x-value increases.increasing - The y-value increases as the x-value increases.
x---decreasing - The y-value decreases as the x-value increases.decreasing - The y-value decreases as the x-value increases.
x---maximum - Highest pointmaximum - Highest point
x---minimum - Lowest pointminimum - Lowest point
x---parabola - A U-shaped graph of a quadratic equationparabola - A curved, U-shaped graph that represents a quadratic equation

4.4:
WITHOUT SOLVING... explain the reasoning you would use to determine which absolute value graph matches the inequality. Remember to write your explanation in your wikispace.
|2x+4|-5>7 matches with graph C. This is because it is an or inequality.
{4.4_journal.jpg} 4.4_journal.jpg