2.3.1: Preparation M.3

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(1) Several years ago, Onondaga Community College, in upstate New York, introduced a meal plan that included “Flex Dollars” that were stored on students’ ID cards. The following description of flex dollars appeared on the college’s website:

To accommodate instances where you do not wish to purchase a “meal”, but would still like something to eat or drink, the College offers $150 of “Flex Dollars” included in each meal plan package. This “flexible money” may be used just like cash for any item sold in the Gordon Café, Mawhinney Café, Starbucks or Fresh Express. Do you want that Large Mocha at Starbucks or that pint of Ben and Jerry’s from Mawhinney Café? Use your flex dollars to pay for it!

Onondaga student Loralee tracked her use of flex dollars weekly during the fall semester as shown in the table below:

Week	Balance on Loralee’s ID Card
0	$150.00
1	$146.75
2	$142.75
3	$139.00
4	$134.00
5	$130.25
6	$126.25
7	$122.25
8	$118.50
9	$114.50
10	$110.00
11	$106.50
12	$101.50
13	$97.00
14	$93.25

(a) On a separate piece of paper, make a graph of the amount of money left on Loralee’s card over the semester. Note: If completing this problem online, follow the instructions given online to create your graph.

(b) This model is approximately linear. What are the units for the slope?

(i) $

(ii) Week/$

(iii) $/week

(iv) There are no units

(d) What is the significance of the horizontal intercept?

(e) Let M be the amount of money left on the card, t weeks after the beginning of the fall semester. Write a linear equation to model the data. Use Week 0 and Week 14 to calculate the slope. Round your slope to 2 decimal places.

(f) If Loralee continues to spend her flex dollars at the same rate, use the equation from part (e) to determine how much money will be on the card at the end of spring semester which also lasts 14 weeks. Use the equation from part (e) to determine the answer.

(2) A teacher surveyed her students about the amount of physical activity they do each week. She then had their body mass index (BMI) measured. The results are recorded in the table below.

Student	Active Hours per Week	BMI
A	10	16
B	3	25
C	6	24
D	8	10
E	10	16
F	8	18
G	7	21
H	2	28
I	19	9
J	14	12

(a) Using a spreadsheet application, make a scatterplot of this data.

Using the scatterplot, create a linear regression model (trendline). Write the equation of the trendline here:

(b) Using the linear model from Question 2(a), estimate the BMI of a student who is active for 12 hours a week. Round your answer to the nearest tenth.

After Preparation M.3 (survey)

You should be able to do the following things for the next collaboration. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Collaboration M.3, you should understand the concepts and demonstrate the skills listed below:

Skill or Concept: I can …	Rating from 1 to 5
identify the slope and the vertical intercept of a linear equation.
identify a linear trend or data that is increasing or decreasing linearly.
use a spreadsheet to make a scatterplot.
create a linear regression model (trendline) using technology.

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