Download Name: AFM Module 3 Lesson 3 Assignment – The Pink Pig Problem

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AFM Module 3 Lesson 3 Assignment – The Pink Pig Problem
Be sure to show your work and demonstrate correct reasoning when appropriate.
Include any graphs or tables that are necessary to support your answers! Type
your answers directly in the document below each question. Make your answers
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the document!!
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.
Use the following link to watch an animation exploring this problem.
http://www.dlt.ncssm.edu/algebra/09_pig_problem/Pig3.html
1. Complete the following table giving the value of the pig after a given
number of weeks.
Number
of weeks
(t)
0 (now)
Value of
pig (v)
1
2
3
4
5
6
7
8
9
10
2. Fit a quadratic model to this data using your calculator. Give the
equation for your model below.
3. 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.) What do these x-intercepts represent?
4. What is the y-intercept of the model? What does this represent in the
context of the problem?
5. What’s the vertex of your equation? (You can find this using the graph
 b  b  
,f
or the formula 
 .) What does the vertex represent in the
 2a  2a  
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.
6. When is the value of the pig equal to zero? Use these values of t 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. Give your model and the graph below.
7. Graph the equation you wrote in step 6 with the equation you found
using quadratic regression on the same set of axes. Show the graph below
and write a couple of sentences comparing the two models.
8. 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. Graph
this model and interpret the x-intercepts and vertex in the context of the
problem.