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# Shannon Golden's Project: Real - World Linear and Exponential Relationships

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on 7 May 2013#### Transcript of Shannon Golden's Project: Real - World Linear and Exponential Relationships

Section 1 Section 2 Equations Equation #1 : Annual Cost of Owning a Cat C = 365 + 670n Equation #2 : Annual Cost of Owning a Dog C = 470 + 580n In both of these equations: N = Number of years C = Total Cost Tables Graph Citation "Pet Care Costs." ASPCA. N.p.. Web. 18 Mar 2013. <http://www.aspca.org/adoption/pet-care-costs.aspx >. Section 3 Equation Equation: Estimated Chicken Population in America since 2010 C = 455 (1.01^n) In this equation: N = Number of years

C = Number of Chickens

(^ = To the power of ) ) ( Graph According to thepoultrysite.com, in 2010, the estimated number of chickens 'on hand' in the US was 455 million birds. This was a one percent increase from the previous year, 2009. If this growth rate continued for the next 10 years, the population will grow exponentially. I have been wanting to get a cat. My mom wants to know what the cost is for actually owning a cat. According to ASPCA.org, the initial costs of getting a cat is $365 (this includes medical treatments and up front supplies). ASPCA also predicts that your annual cost for food, recurring medical situations, litter, etc. will be about $670. My mom, after looking at the costs of a cat, suggested we look at getting a small dog. On the ASPCA website, it says, the initial costs of a small dog is about $470 (this includes medical treatments, training, and up front supplies). The predicted annual cost of owning a dog is about $580 (food, toys, medical, etc.) Examples of a Real-World Linear Relationships . C = 470 + 580n C = 365 + 670n POI Finding the POI 365 + 670n = 470 + 580n -580n -580n 365 + 90n = 470 +365 +365 90n = 115 90 90 n = 2 1/3 So, at about 2 years, four months, both a dog and a cat would cost the same amount of money ( approximately $1,106.) Graph Example of Real-World Exponential Relationship Citation "U.S Chicken and Eggs Annual Summary 2010." The Poultry Site. N.p., n.d. Web. 19 Mar 2013. <http://www.thepoultrysite.com/articles/1951/us-chickens-and-eggs-annual-summary-2010>. Recognizing Linear and Exponential Situations Linear Situations Linear situations are situations in which there is a constant rate of change between two variables. On a graph, a linear relationship is expressed through a straight line. Exponential Situations An exponential situation is an either decreasing of increasing pattern. It can be found by multiplying the previous value by a factor bigger than one (if increasing) and smaller that one (if decreasing.) On a graph, an exponential situation is show as a curved line. Finding the slope of a Table and graph for Linear Models Finding the slope for a linear model using a graph or an equation is fairly easy. Using a Graph: Here is an example table describing the number of candy bars Joe sells in five days. Step One: Step 2: Pick two points on the graph and put them in the order of Y2 Y1

X2 X1 - My two points (1, 12) and (2, 24). Y2 Y1 X2 X1 24 12

2 1 - Step 3: do the math ( subtract Y2 and Y1 and X2 and X1) then divide the fraction). 24 12

2 1 - = 12

1 = 12 So, the slope is 12! Using a Table: Step 1: Pick two points. Step 2: Subtract them. 48

-12

36 Step 3: Divide that by the difference of the two points' X values. 4

- 1

3 36 / 3 = 12 So, your slope is 12! Finding Growth and Decay Factors From a Table and Graph for Exponential Models Using a Graph: Step 1: Choose one point Step 2: Divide that point by the previous point 54 / 18 = 3 So, the slope is 3. Using a Table: Step 1: Same as the Graph, choose a point. Step 2: Divide that point by the previous one. 54 / 18 = 3 So, the slope is 3. Keep in mind that if your answer is more than one it is a growth factor and if it is less than one, you are dealing with a decay factor The Slope-intercept Form of a Linear Equation y = m + b x Slope Y - Intercept Y - Value X - Value This SLOPE - INTERCEPT form shows represents the constant rate of change in all linear relationships, by showing the slope. General Form of an Exponential Equation y = b (m ) x Y - Value Y - Intercept Growth Factor X - Value This exponential equation represents the multiplication aspect of an exponential relationship (hence the m^x). Cat Dog Exploring Real-World Linear and Exponential Relationships VS. Through this information an exponential relationship can be seen between the number of chickens and the number of years. By using this information about the annual cost of owning a dog verses owning a cat, a linear relationship is expressed. Throughout this project you will see several explanations of various linear and exponential functions, as well as two example of linear relationships and one of an exponential relationship. I hope you enjoy my project. Introduction Thanks For Reading!!!

Full transcriptC = Number of Chickens

(^ = To the power of ) ) ( Graph According to thepoultrysite.com, in 2010, the estimated number of chickens 'on hand' in the US was 455 million birds. This was a one percent increase from the previous year, 2009. If this growth rate continued for the next 10 years, the population will grow exponentially. I have been wanting to get a cat. My mom wants to know what the cost is for actually owning a cat. According to ASPCA.org, the initial costs of getting a cat is $365 (this includes medical treatments and up front supplies). ASPCA also predicts that your annual cost for food, recurring medical situations, litter, etc. will be about $670. My mom, after looking at the costs of a cat, suggested we look at getting a small dog. On the ASPCA website, it says, the initial costs of a small dog is about $470 (this includes medical treatments, training, and up front supplies). The predicted annual cost of owning a dog is about $580 (food, toys, medical, etc.) Examples of a Real-World Linear Relationships . C = 470 + 580n C = 365 + 670n POI Finding the POI 365 + 670n = 470 + 580n -580n -580n 365 + 90n = 470 +365 +365 90n = 115 90 90 n = 2 1/3 So, at about 2 years, four months, both a dog and a cat would cost the same amount of money ( approximately $1,106.) Graph Example of Real-World Exponential Relationship Citation "U.S Chicken and Eggs Annual Summary 2010." The Poultry Site. N.p., n.d. Web. 19 Mar 2013. <http://www.thepoultrysite.com/articles/1951/us-chickens-and-eggs-annual-summary-2010>. Recognizing Linear and Exponential Situations Linear Situations Linear situations are situations in which there is a constant rate of change between two variables. On a graph, a linear relationship is expressed through a straight line. Exponential Situations An exponential situation is an either decreasing of increasing pattern. It can be found by multiplying the previous value by a factor bigger than one (if increasing) and smaller that one (if decreasing.) On a graph, an exponential situation is show as a curved line. Finding the slope of a Table and graph for Linear Models Finding the slope for a linear model using a graph or an equation is fairly easy. Using a Graph: Here is an example table describing the number of candy bars Joe sells in five days. Step One: Step 2: Pick two points on the graph and put them in the order of Y2 Y1

X2 X1 - My two points (1, 12) and (2, 24). Y2 Y1 X2 X1 24 12

2 1 - Step 3: do the math ( subtract Y2 and Y1 and X2 and X1) then divide the fraction). 24 12

2 1 - = 12

1 = 12 So, the slope is 12! Using a Table: Step 1: Pick two points. Step 2: Subtract them. 48

-12

36 Step 3: Divide that by the difference of the two points' X values. 4

- 1

3 36 / 3 = 12 So, your slope is 12! Finding Growth and Decay Factors From a Table and Graph for Exponential Models Using a Graph: Step 1: Choose one point Step 2: Divide that point by the previous point 54 / 18 = 3 So, the slope is 3. Using a Table: Step 1: Same as the Graph, choose a point. Step 2: Divide that point by the previous one. 54 / 18 = 3 So, the slope is 3. Keep in mind that if your answer is more than one it is a growth factor and if it is less than one, you are dealing with a decay factor The Slope-intercept Form of a Linear Equation y = m + b x Slope Y - Intercept Y - Value X - Value This SLOPE - INTERCEPT form shows represents the constant rate of change in all linear relationships, by showing the slope. General Form of an Exponential Equation y = b (m ) x Y - Value Y - Intercept Growth Factor X - Value This exponential equation represents the multiplication aspect of an exponential relationship (hence the m^x). Cat Dog Exploring Real-World Linear and Exponential Relationships VS. Through this information an exponential relationship can be seen between the number of chickens and the number of years. By using this information about the annual cost of owning a dog verses owning a cat, a linear relationship is expressed. Throughout this project you will see several explanations of various linear and exponential functions, as well as two example of linear relationships and one of an exponential relationship. I hope you enjoy my project. Introduction Thanks For Reading!!!