Lesson Plan #6
Lesson Plan #019
Class: PreCalculus Date: Wednesday October 17th, 2012
Topic: Mathematical Modeling
Aim: How do we use mathematical models to approximate sets of data points?
Objectives:
1) Students will be able to use mathematical models to approximate sets of data points
HW# 019: Page 124 #’s 8, 12, 16, 20, 26, 30, 36, 42,
Page
Do Now:
The table at right lists the total tuition, room and board rates charged for
full-time undergraduate students in degree-granting institutions. Let’s plot these points
on a graphing calculator. We’ll use 1 for year 2001.
On your graphing calculator press the [STAT] button. On the Edit Menu, press 1. Edit. Move the cursor to the top of L1. Press [CLEAR] and press . Do the same for L2. Go back to L1, in the first line for data enter 1 then down and enter 2, so on and so forth until you get to 11. Starting at the top of L2, enter the cost of tuition; for $13,393 enter 13.393. Go to [Y=] and turn off any equations there from graphing. Then press 2nd [Y=] which takes you to STAT PLOT. Make sure it is ON, points, XList: L1, YList: L2, Mark is the little box.
Then Zoom 9 to see the plots.
What kind of graph is this (linear, quadratic, exponential, etc.)?
Procedure:
Write the AIM and DO NOW
Get students working!
Take attendance
Give back work
Go over HW
Collect HW
Let’s try to find an equation of a line that best fits the data.
Go to STAT, CALC, 4:LinearReg(ax+b), L1, L2, Y1. So your equation is now stored in Y1. Use 2nd Calc, then Value to calculate the estimated cost in 2012, 2013
Example:
In Pennsylvania, the state income tax is directly proportional to gross income. You are working in Pennsylvania and your state income tax deduction is $46.05 for a gross monthly income of $1500. Find a mathematical model that gives the Pennsylvania state income tax in terms of gross income.
Exercise #1: Variable M varies directly with p. If M = 75 when p = 10,find M when p = 16.
Exercise #2: Variable Y varies jointly with P and Q. If Y = 144 when P = 12 and Q = 8,find Y when P = 15 and Q = 25.
Exercise #3: Variable T varies directly with the square of m. If T is 8 when m = 2,find T when m = 4.
Example #4: R varies inversely with variable T. If R is 168 when T = 24, find R when T = 30.
Example #5: A video store rents DVDs, and the weekly total number varies directly with the total inventory, and varies inversely with the cost of each rental tape. The store in Acme, NY, last week rented a total of 3000 DVDs when its inventory was 9600 and the cost per rental was $2.40. If its inventory does not change, what would be the effect on the weekly total number of increasing the cost per rental to $3.00?
Example #6:
Example #7:
Example #8:
Example #9:
[pic]
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Year Cost
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