Math Help - Quantititive Reasoning

QUESTION 1

Year	Data Set A	Percentage Growth for Set A	Data Set B	Percentage Growth for Set B
1970	3		4
1975	20		370
1980	128		752
1981	186		834
1982	270		910
1983	391		996
1984	567		1056
1985	822		1126

Part A: Determine the percentage growth for each data set. Round each percentage to the hundredth place. Part B: Which data set is exponential, if any?

· Set A

· Set B

· Both

· Neither

Part C: Create a graph of the data set you chose in Part B in your notebook and include a justification for Part B your answer choice. Upload your graph and justification. 

Part D: Determine the anticipated value for 1986 datum for the exponential data set. 

QUESTION 2: The following data presents the number of transistors per chip for Intel computer chips between 1971 and 1995.1 Moore’s Law predicts that these values will grow exponentially. Let’s check on the accuracy of Moore’s Law.

Year	Chip Model Name	Number of Transistors per Chip
19711971	Intel 4004	23002300
19721972	Intel 8008	35003500
19741974	Intel 8080	45004500
19761976	Intel 8085	65006500
19781978	Intel 8086	2900029000
19821982	Intel 80286	134000134000
19851985	Intel 80386	275000275000
19891989	Intel 80486	11802351180235
19931993	Intel Pentium	31000003100000
19951995	Intel Pentium Pro	55000005500000

Part A:   What was the rate of growth in transistors from 1971 to 1972?

 transistors per year

Part B:   What was the rate of growth from 1982 to 1985?

 transistors per year

Part C:   What was the rate of growth from 1993 to 1995?

 transistors per year

Part D:   Which of the following best describes the growth rate of transistors? •

a. It appears approximately exponential

b. It appears approximately linear

c. Neither

QUESTION 3:

Bald Head Island (BHI) is one of the islands in the Smith Island Complex. Each fall from 1999 to 2012, a conservatory on the island estimated the white-tailed deer population. The estimates are shown in the graph below. Part A: During which two-year period (or periods) was the deer population increasing? Select all that apply.

· 1999 - 2001

· 2001 - 2003

· 2003 – 2005

· 2005-2007

· 2007-2009

Part B: During which two-year period (or periods) was the deer population decreasing? Select all that apply.

· 1999 - 2001

· 2001 - 2003

· 2003 - 2005

· 2005-2007

· 2007-2009

Part C: What is happening to the deer population between 2007 and 2009?

· Decreasing and then increasing

· Increasing

· Increasing and then decreasing

· Decreasing

· None of the above

QUESTION 4:

A company has 100 employees who were asked to make a donation to this year’s emergency office fund. The memo asked all employees to donate over three weeks (15 work days). The data show the  cumulative number of employees who made their donations. (For example, on Day 2, five more employees made donations [12 – 7].)

End of Day	Cumulative Number of Donations
1	7
2	12
3	19
4	28
5	39
6	51
7	62
8	72
9	80
10	87
11	92
12	95
13	97
14	98
15	98

Part A: How many donations were made on made on the Day 15?

Day 15 donations =  Part B: In relation to the data in Column B (the cumulative number of employees who have contributed), what day had the most donations? Day . Part C: Open  QR_11A_Spreadsheet_Practice . Be sure you are on the Emergency Fund tab. In Column C of the spreadsheet, beginning in Cell C3, enter a formula to find the number of new donations each day. (Tip: Think about your process from Part B.) Which of the following is the best description of the new data?

· It increased for a while and then decreased.

· It increased by a larger and larger amount each day.

· It increased by a larger amount each day for a while and then continued to increase but by smaller amounts.

Part D: Now you will make a scatterplot, either by hand in your notebook or by using the Chart feature in   QR_11A_Spreadsheet_Practice. If you use the spreadsheet feature, print out a copy of the scatterplot for your notebook. If you sketch by hand, take a picture to upload. Complete each of the following steps: • First, make a scatterplot of the original (cumulative) data. • On the same scatterplot, include the data for each day's donations. Look to see whether your answer to Part C makes sense with the graph of the new data. • Upload your graph.

Part E: Which is the best description of the cumulative donations from Day 1 through Day 5?

· The cumulative donations increased, but the amount of increase got smaller.

· The cumulative donations increased by ever larger amounts.

· The cumulative donations increased by the same amount each day.

Part F: Which is the best description of the new donations from Day 1 through Day 5?

· The new donations increased, but the amount of increase got smaller.

· The new donations increased by ever larger amounts.

· The new donations increased by the same amount each day.

Part G: Describe the cumulative data and graph prior to and after Day 6. Select all that apply.

· Before Day 6, the cumulative donations increased at ever larger amounts.

· After Day 6, the graph was concave down.

· After Day 6, the cumulative donations decreased.

· Before Day 6, the graph was concave down.

QUESTION 5, 8 PRAC:

Suppose your water intake changes, according to the pattern presented in the data table below.

Week	Daily Water Intake in Ounces
0	67
1	64
2	61
3	58
4	55
5	52

Part A:

What pattern do you notice in the water intake values? The water intake values are

a. increasing

b. decreasing

c. neither increasing nor decreasing

and the change is --------- ounces per week.

PART B:

Part C:

What is the slope between any two points in the data? Slope =

Part D:

What are the coordinates of the 𝑦-intercept of the graph?

Part E:

Write an equation representing this relationship in slope-intercept form.

QUESTION 6:

You determined a formula for the value of a car based on the age of the car, assuming that the relationship was linear. Suppose you plan to purchase a new car after selling the old car from the class activity for scrap. Assume that new cars will have increased in price, so plan to spend $22,500.

Remember that the car was projected to last for 8 years and be worth $500 in scrap value.

Part A:

How much do you need to save if you want to pay cash for your next new car?

Total amount to save = $

Part B:

How much money should you save each year in order to have sufficient cash to buy the car? (Assume that no interest is being paid on the savings; therefore, ignore any interest calculations.)

Amount to save per year = $

Part C:

Write an algebraic equation expressing the relationship between the total amount of money saved for the new car and the number of years that have passed. Let t represent the number of years, and let S represent the amount of money saved.

Part D:

Is the relationship between the total amount of money saved and the year proportional?

No

Yes

Part E:

Do you think it would work to save money "once per year," as we've been describing, or would saving each month be better? Write the equation that describes saving every month. Let t represent the number of months, and let S represent the amount of money saved.

Question 7:

We know that cars lose value as the total mileage increases.  How does this mathematical relationship work? Is it linear?  We will explore this question in this problem.

You can find out the current value of a car using the Kelley Blue Book website. This resource is available online at www.kbb.com. Suppose you are selling a 2014 Chevrolet Impala LTZ Sedan 4D. The car is in excellent condition and only has standard options. During the summer of 2014, the Kelley Blue Book website yielded the following values:

Mileage	Value, in dollars ($)
10,000	31,943
15,000	31,427
20,000	30,977
25,000	30,453
30,000	29,988
35,000	29,471

Part A: Is the relationship between value and mileage linear? Pick the best response and justification below.

· Yes, because the rate of change is not constant.

· No, because the rate of change is constant.

· No, because the rate of change is not constant.

· Yes, because the rate of change is constant.

Part B:

Sketch a graph of the relationship between the value of the car and the mileage in your notebook. If you like, you may use a spreadsheet. Does your graph appear to be the graph of a linear relationship? Yes or No

Question 3 is a great representation of the difference between formal and practical mathematics. When we use the slope formula for Part A, we get answers that are not equivalent. However, the differences are very slight. The car is decreasing in value approximately $500 for each additional 5,000 miles.

Visit the   Kelley Blue Book website and determine the value of your car or a car you would like to own. If you do not have a car, check the value of a 2012 Ford Mustang. Assume the following conditions:

73,000 miles

Deluxe convertible two-door

Standard equipment

Selling to a private party (not a dealer)

In "very good" condition

Describe the car and give the value shown on the website.

QUESTION 8

The principal of compounding applies to more than just bank accounts. One context that involves compounding is salary raises. When you earn a raise on a salary each year, your raise is applied to the previous year's salary.

To make this example concrete, suppose you start with a salary of $40,000 per year. You receive a 2.25% raise each year.

Part A:

Write an algebraic equation whose input is the year (t) and whose output is your salary (S) in that year.

Part B:

What would your salary be in 8 years? Round to the nearest whole dollar, if needed. $-------

QUESTION 9

In this practice assignment, you will use spreadsheet regression or the online regression calculator at   http://www.alcula.com/calculators/statistics/linear-regression to examine the relationship between average annual income and average life expectancy in a country. This relationship is called the Preston curve.

Open  QR_8D_Spreadsheet_Practice , which gives the average annual income and average life expectancy in 25 low-income countries. Each row corresponds to a country. Use technology (spreadsheet regression or the Alcula website given above) to create a scatterplot and regression equation for the Preston curve data. Round all answer values to the nearest ten thousandth (the fourth decimal place). Part A: Slope =  Part B: Choose the best interpretation of the slope.

· Living longer causes you to make more money.

· Average Income increases 14 cents for every additional year that you live.

· Making more money causes you to live longer.

· Average Life Expectancy increases 0.0014 years for every additional dollar of average income.

Part C: Determine the correlation coefficient. Note that you may have to change your settings if your technology did not already report this value. Correlation coefficient =  Part D: The coefficient of determination (R2) is found by squaring the correlation coefficient (r).

The coefficient of determination =  Part E: Choose the best interpretation of the coefficient of determination.

a. About 70% of the variation from the predicted value for Average Income is due to changes in Average Life Expectancy.

b. About 70% of the variation from the predicted value for Average Life Expectancy is due to changes in Average Income.

c. Less than 1% of the variation from the predicted value for Average Income is due to changes in Average Life Expectancy.

d. Less than 1% of the variation from the predicted value for Average Life Expectancy is due to changes in Average Income.

QUESTION 10: Information only: Statisticians typically look at how good the fit is and whether the mathematical model makes sense for the physical situation or scenario. An example of a regression for a power model is shown below. Notice the curve. An example of a regression for a power model is shown below. Notice the curve.

In In-Class Activity 8.D, you investigated the relationship between the global temperature anomaly and the amount of carbon dioxide in the atmosphere from the burning of fossil fuels. The two scatterplots that follow break the data down further to investigate the relationships between global temperature anomalies and coal emissions and global temperature anomalies and motor gasoline emissions.

Part A: Use the coefficient of determination to decide which energy type has a stronger association with global temperature anomalies.

· Coal Emissions

· Motor Gasoline Emissions

· there is not enough information to tell

· neither coal nor motor gasoline

Part B: What percentage of the changes in global temperature anomalies can be attributed to changes in motor gasoline emissions? Round to the nearest whole percentage point. Answer = %