1. Unit Conversions

INSTRUCTIONS: The Kelvin scale is the scale most widely used to indicate temperatures in space and is the basic temperature unit in science. It is denoted with a K and the word "degrees" is not used with it. The conversion from Kelvin to Fahrenheit is done by multiplying the temperature in Kelvin by 1.8 then subtracting 459.67. The temperature on Mars ranges from about 140 K ("140 Kelvin") to about 300 K ("300 Kelvin"). Assume you are a new astronomy student and you are still getting used to the Kelvin scale. 1) Make a table with several reference values for converting common temperatures on Mars from Kelvin to degrees Fahrenheit, then 2) make a linear graph which can help you make reasonable approximations for what the temperature in Fahrenheit is based on the temperature given in Kelvin. (Hint: Start at 140 K in the table and move up by steps of 20 K until you get to 300 K.)

2. Oscar Winners

INSTRUCTIONS: The ages (in years) of Academy Award (Oscar) winners for Best Actress and Best Actor are given. Compute the 1) various measures of typicality, 2) measures of spread, and, if you'd like, measures of relative standing to help you determine if there appears to be a big difference between the ages of actresses and actors when they win an Academy Award. Then, 3) write a summary of your conclusion in the box below, making sure to reference the quantitative data to support your point. (Hint: If the mood so strikes, making a graph such as a histogram and/or boxplot can only help your case.)

3. Interest

INSTRUCTIONS: When you graduate, your family members have promised to give you some money as you start out in your new life. They will give you $5000 to use as you wish. Being a financially responsible quantitative reasoner who already has a job in their chosen career (because you're talented and your skills are so incredibly marketable), you're not worried about your finances for the near future, at least. You decide to invest in a savings account. There are two options available to you. First, you could invest in an account that accumulates simple interest of $10/month. There is a special promotion that gives you a bonus of $1000 when you open the account, given that the bonus is also deposited in the account and you never take any money out of it for at least 10 years. The second option is that you may accumulate 6% annual interest, compounded monthly. There is a special promotion that gives you a bonus of $300 when you open the account, given that the bonus is also deposited in the account and you may never take any money out of it for at least 10 years. 1) Determine the amount of time it takes for the compound interest option to be better than the simple interest option by writing formulas describing how the interest in each option grows monthly. 2) Determine when you will have $10,000 in each of the different cases. Write your answers in the box below. (Hint: Be sure to LOCK any formulas you use and to make sure you exponents are right based on the fact that the time in the A column is given in months, not years. Also note you may have to extend the time column to show a greater range of months.)

4. Models

INSTRUCTIONS: The table to the left shows the CDKO Index Value which describes the inflation rate of the British pound, given for every 5 years from 1903 on, found on the UK's Office for National Statistics website. (Note that the inflation indices for the British pound are a bit more complex and less accurate than the United States' CPI Index Value for reasons that you will have to ask someone with more international financial knowledge than your Quantitative Reasoning professor. These are not official National Statistics, I understand, but are somehow reasonable approximations. I guess.) 1) Make a plot of the index values over time and choose, and fit, the most appropriate model to the graph, making sure to include the equation and R-sqaured value. 2) Use the equation for the fitted trendline to determine the rate at which the British pound typically inflates. 3) Use your answer for part 2 to determine what the approximate index value will be for 2014 and for 2024. Do these predictions seem reasonable? Explain in the box below.