Question 1050280: The Problem: Farmer Fay has a pig that presently weighs 200 pounds. She could sell it now for a price of $1.40 a pound. The pig is gaining 10 pounds a week while the price per pound of pork is dropping 2 cents a week.
The table below is the value of the pig after a given number of weeks.
Number of weeks (t ) 0,1,2,3,4,5,6,7,8,9,10
Value of pig (v) in dollars 280,289.80,299.20,308.20,316.80,325,332.80,340.20,347.20,353.80,360
Fit a quadratic model (STAT - CALC - 5:QuadReg) to this data using your calculator. Give the equation for your model below in standard form. (y = ax2 + bx + c)
2a. What are the x-intercepts of your model? (Use the graph on your calculator to find or estimate them, don’t try and find them from the equation.)
2b. What do these x-intercepts represent?
3a. What is the y-intercept of the model?
3b. What does this represent in the context of the problem?
4a. What’s the vertex of your equation? (You can find this using the graph or the formula .)
4b. What does the vertex represent in the context of the problem?
Now that we’ve found the model (in standard form) using quadratic regression, let’s write a model ourselves and compare them.
We’ll use factored form to write the equation.
Use the x-intercepts found in Question 2 to write the equation of the model in factored form. Graph this equation on the same screen your plotted your data on earlier. Adjust a if necessary to get it to be a good fit.
a. Give your model. It will be in the form y = a(x - b)(x - c).
b. Insert the graph below.
Graph the equation you wrote in step 6 with the equation you found using quadratic regression in Question 2 on the same set of axes.
a. Insert the graph below.
b. Write a couple of sentences comparing the two models.
What if we account for the cost of feeding the pig? Adjust your model from step 6 to account for the fact that pig feed costs $5 a week.
a. Write the equation for the adjustment to feed the pig.
b. What are the new x-intercepts and what do they mean in the context of the problem?
c. What is the new vertex and what does it mean in the context of the problem?
Answer by ikleyn(52776)   (Show Source):
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