MA105

Each Question Should be Answered in AT LEAST 75 words A PIECE.

1. Pick a company whose sales you want to model and predict. Look up their sales information and pick 2 years of data. Using that information, create a linear equation that can be used to predict the sales of the company. Once you have your equation, predict the sales 2 years from now. Make sure you include in your post the links where you found the relevant information. Clearly show your work. This includes naming the company, sharing the ordered pairs, defining variables, finding the slope, determining the equation, and then using that equation to predict.

2. Which of the equations or inequalities this week did you enjoy solving the most and why? Which were the most challenging? Did you come across problems in the text that you need help solving? If so, include them here. Try to find an interesting example of your most challenging equation/inequality type being used in the real world. Why is the example interesting? What is the specific equation used in that situation? Include links to the sources.

3. Rideshare companies such as Uber and Lyft often charge a flat fee, in addition to per mile rates and other fees. Other cab companies may include per minute rates in addition to the per mile and pickup charge. Using your own experience or some Internet research (ride.guru or taxifarefinder.com are great resources): Write an equation that represents the rideshare or cab company's rate for your area. Is this a function? Why or why not? Using that equation, how much would it cost to go from your home to your job or other important location? Which of the parent equations covered this week does your equation match? What transformations were done to it to get your equation?

4. One real-world example of a degree-two polynomial is the projectile motion equation used in physics:Details about this formula can be found at the  brainfuse.com website . For example, if you hit a baseball at shoulder height (say about , you may have an initial velocity of around. The force of gravity is about . We can convert our miles to hour to feet per second (89.5 mph = 131.3 ft/s) and create an equation that would model the height of the ball at time t:

Pick a baseball team average speed off the bat from  this list . Pretend you are on that team and hitting a pitch. Using your height and the information in the table, create your own personalized equation as was done in the example above.

Once you have your equation, find the zeros and the vertex using the techniques covered this week in Chapter 3. Show all your work! Do you think the difference is more from the difference in initial height of the bat or in the speed of the pitch?

5. Rational functions can show up in surprising places. For example, when you are finding the average, you are actually using a rational function!

Or in math speak,

 

Often when making an expensive purchase we look at the total cost and whether we are willing to pay it. Another way to consider this is to find the average cost per month to see if it is in your budget.

A common example would be when you renew the contract on your cell phone. Often we buy a new phone at the same time, and you can either pay it up front or have it added to your monthly bill.

If you pay for the device up front, you can use the following function to model the monthly cost, where m is the number of months you plan on owning the device.

 

Do some research to find the cost of a device you want to buy, and either your actual monthly bill or an advertised monthly bill. Using these numbers, give us the function you would use to model the monthly cost.

Based on the asymptotes, what would be the minimum monthly average cost for this phone and plan? Explain how you got your answer.

What would be the average cost if you replace the phone after 2 years (24 months)? Does this make you reconsider the price of the phones you buy?

Compare your classmates' functions to your own. Do you think it's the cost of the phone or the monthly cost of the phone plan that makes the most difference?

6. You were introduced to the Euler's number e, a mathematical constant. Another well-known constant is pi. Do some research on other important constants in mathematics. A good constant has a specific name and is important in mathematical formulas. Do not choose pi or e. Share what you have found out about the number; for example, its history, some trivial facts about the number, and/or how it is applied. Be sure to include your sources so others can do further research. To get you started in your research, below are some sources you can use: http://www.popularmechanics.com/flight/g163/13-most-important-numbers-in-the-universe/ https://en.wikipedia.org/wiki/Mathematical_constant#Table_of_selected_mathematical_constants