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C o m p a r i s o n O fH o m e H e a t i n gS y s t e m sJonathan NakaStudent Sample

http://www.stltoday.com/blogzone/the-birds-nest/tag/weather

ObjectivesAfter this project, we should be able to have a method for solving algebraic linear equations. We will be able to calculate the rate-of-change (or slope) of a linear model and apply it to an equation. In addition, we will enhance our 21st century skills inside and outside of the classroom.

We will also become familiar with creating a PowerPoint, drawing up graphs and searching the internet for information regarding our project.

CFQsEssential Question How can math be applied to the real world?

Unit QuestionsWhy is math so important?How can utilizing variables and symbols help you understand a real world application?What occupations do you think require math?

Content QuestionsHow can the rules of mathematics can be used to help solve the real world problem?Why is Linear Relationships so important to Math?A linear relationship is a special relationship between two things that have some number value. We can apply math to compare things such as speed, distance, time, weight, temperature, value, quantity, percent, etc. If it is measureable, it can have a linear relationship.

If we take the number value and plot points on a graph using these things (variables) and if these points create a straight line on this graph, then the relationship is linear.

ProblemWe want to install a heating system in our home. We can choose an Electric heating system or a Gas heating system. The Electric system is more expensive to install, but the less expensive to operate. The table shows the total cost you will pay for each heating system after a 10 year period. Total Cost (y)Years (x)ElectricGas05,00012,000510,50015,5001016,00019,000We want to see which system will cost us less after 40 years of operation.We let, y is the total cost ($) of each heating system x equal the number of years of operation.Total Cost (y)Years (x)ElectricGas05,00012,000510,50015,5001016,00019,000First, we set up a linear equation for both heating systemsElectric:yE = mEx + 5,000 Gas:yG = mGx + 12,000Step 1Step 2Now, we find the rate-of-change for each equation (m)mG = 19,000 15,500 10 5 mG = 700mE = 16,000 10,500 10 5 mE = 1,100Total Cost (y)Years (x)ElectricGas05,00012,000510,50015,5001016,00019,000Now, we substitute our rate-of-change into our equationsElectric:yE = 1,100x + 5000 Gas:yG = 700x + 12,000Step 3Step 4Now that we have our equations, we can calculate the total cost of each heating system after 40 years (x = 40)Electric:yE = 1,100(40) + 5,000 yE = 49,000 Gas: yG = 700(40) + 12,000 yG = 40,000Step 5Now, we can graph the two equations where we can clearly see that even though the Gas heating system costs more to install, after 40 years it will be be cheaper than the Electric heating system.Total Cost (y)Years (x)ElectricGas05,00012,0001016,00019,0002027,00026,0003038,00033,0004049,00040,000Helpful LinksGet some Math help! www.mathsteacher.com.au http://www.youtube.com/watch?v=JsA16TF7LuU

Need help creating graphs and charts? http://42explore.com/graphs.htm

Create a Chart or Graph in Excel http://office.microsoft.com/en-us/excel/HA102004991033.aspx