Question
Sam's Enterprises has two retail locations one in Collingwood and one in Victoria.CPI Index Base Year 2002172.9 Base year 20022002 Last Year 775,995 S 973,545 445,873 S 773,998Collingwood VictoriaDeflate Last Year's Sales for Collingwood and Victoria Did either location experience sales growth last year compared to the base?
Sam's Enterprises has two retail locations one in Collingwood and one in Victoria. CPI Index Base Year 2002 172.9 Base year 2002 2002 Last Year 775,995 S 973,545 445,873 S 773,998 Collingwood Victoria Deflate Last Year's Sales for Collingwood and Victoria Did either location experience sales growth last year compared to the base?
Answers
In the last decade or so there has been a dramatic expansion of small retail convenience stores (such as Kwik Shops, 7 Elevens, Gas 'N Shops), although their prices are generally much higher than prices in large supermarkets. What explains the success of the convenience stores?
Were given to data points about the year and the number of J. C. Penney stores. And we can use those two data points to find the equation that relates them. And our variables are t for the number of years and or for the year number and end the number of stores. So let's start with our Slope 1067 minus 1078 divided by seven minus three. And that gives us negative 11 4th negative because the number of stores is going down. And then let's use our point slope form. Why minus y one equals M times X minus X one and weaken substitute. If we want to use the first point, it doesn't matter which. But if we do, we can substitute 1078. And for why one? We have our slope and we can substitute three and four x one. We're going to simplify this equation, distribute the negative 11 4th and then we're going to add 1078 to both sides. Let's see what that is as a decimal. So we have 1078 plus 33 4th 1086.25 And now if we want to use the variables for the problem, we had n for the number of stores and we had tea for the year. So there's a linear equation that models the situation. Now we're going to use that model to predict the number of stores in 2012 and 2014 2012 would be t equals 12 so we can substitute that into the equation. They gave 11 4th times 12 let's 1086.25 and we get 1053.25 So approximately 1053 stores and then for the year 2014 will do the same thing will multiply negative 11 4th by 14 and we add 1086.25 and we have and is 1047.75 So that would be approximately 1048 stores. Whether or not these answers air reasonable depends on a lot of other factors that we may not be able to predict, such as about the economy. And an example of that is right now as I speak, it's the year 2020 and we're in a pandemic and a lot of stores are closing, and I think JC Penney is in real trouble. So this model that we found here is probably not accurate anymore, and it may not have been accurate in the year 2012 or 2014 either.
See if this works.
In this problem, we're going to find the midpoint between the two points given as a way to estimate the sales in the year 2005. So to get the midpoint, we average the X coordinates 2003 plus 2007 divided by two and we average the Y Coordinates 4174 plus 4656 divided by two. And that gives us 2005. So this is our estimate for the sales in the year 2005 and 4415. So remember that in millions. So in the year 2005 it would be an estimate that the sales were 4415 million dollars.
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