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Math 105A Track A-Mathematical Business Scenarios

Track A: Mathematical Business Scenarios

Scenario 1 (College algebra. Graphs and models 3rd page 180)The Price for a certain type of diamonds are given below.Weight (carats) Price (US Dollars $)0.5 13400.6 17600.7 25400.8 33500.9 41301.0 4920Scenario 2 (college algebra and applications for business and life sciences 2e page 257A manufacturer has daily production costs (in dollars per unit) as given in the table below where is 𝑦 𝑥the number of units producedX (number of units produced)Y (Manufacturing Cost in $ per unit)0 7005 658.7510 62515 598.7520 58025 568.7530 56535 568.7540 580
45 598.7550 62555 658.7560 700Scenario 3The US department of Energy has provided the following data explaining how the Fuel Economy (mpg) changes against the speed (mph) of a medium sized car.Speed (mph) (x) Fuel Economy (mpg) (y)10 17.620 24.130 28.640 31.150 31.760 30.270 26.780 21.3Scenario 4The following table shows the profit from the sale of public address systems and the number of units produced. Here is the number of units produced and is the profit in $.𝑥 𝑦Units Produced Profit5000 36750010000 109500040000 514500070000 8655000100000 11625000
130000 14055000160000 15945000190000 17295000220000 18105000250000 18375000280000 18105000310000 17295000340000 15945000Scenario 5The state is trying to build a rectangular picnic area with one of the longer sides bordering a lake. Fencing is needed for the three sides not bordering the lake. Let (in feet) be the width (shorter side) 𝑥 of the picnic area and let (in feet) be the area of the picnic area. The final goal of this project is to find 𝑦the dimensions which will maximize the area if the state has only budgeted only $6000 to buy the fencing at $10 per linear foot
Scenario 6 A small college currently is trying to increase the tuition. It realizes from historic data that a $10 increase in the tuition rate per credit hour will result in 100 fewer credit hours taken by students each semester. The current tuition is $400 per credit hour. The school has 2000 students and a total 24000 credit hours are taken each semester.Let the revenue per semester in US$ by and let , be the number of $10 increments of the tuition 𝑦 𝑥rate . Scenario 7 Suppose you owe $800 on your credit card and decide to pay only the minimum payment each month. The balance $ that you will have after months is given by the equation 𝑦 𝑥𝑦= 800(0.9898)𝑥
Scenario 8The following table shows how the average price of a house located in Northeastern United States changed during the period 1987-1995. Let be the number of years after 1987 and y be the average 𝑥price in tens of thousands of dollarsYears after 1987Cost of a house (in thousands of Dollars 0 1401 1492 159.63 1594 155.95 1696 162.97 1698 180Scenario 9 An owner of a barbecue grill store has found out at a price per grill, grills can be 𝑝(𝑥) = 150 𝑥/4 𝑥sold for a week. Let in dollars be the weekly revenue that the store will obtain if the weekly demand is 𝑦 dollars.𝑥
Scenario 10 (Adapted College Algebra with Applications for Business and Life Sciences, 2e)A company that produces calculators estimates that the profits (in dollars) from selling a particular 𝑦model of calculator was:𝑦= 152𝑥3 + 7545𝑥2 169625 0 𝑥45Where was the advertising expense (in tens of thousands of dollars)𝑥
Scenario 11 (College algebra make it real page 2820)In 2001, adjustable rate mortgages (ARMs) were offered at different rates at different times of the year. Let be the month of the year ( being January) and let interest rate (percent) for that month. 𝑥 𝑥= 1 𝑦Then can be written as a function of as:𝑦 𝑥𝑦= 0.0008𝑥4 0.0208𝑥3 + 0.177𝑥2 0.6705𝑥+ 7.2331
Scenario 12 (College algebra with applications for business and life sciences 2e page 281)When selling a certain commodity, the profit obtained depends on the advertising cost.The following equation shows how the profit (in US $) varies with the advertising cost (in tens of 𝑦 𝑥thousands of US$) when selling a certain sports equipment𝑦= 141𝑥3 + 5358𝑥2 76560 0 𝑥35

Part One

The task for Part 1 asks students to set up functions based on the raw data provided in scenarios 1, 2, 3, 4, and 8. The results should be completed in a Microsoft Excel spreadsheet file, with each sheet containing one scenario (in all, there should be 5 sheets within the same excel file). All 5 sheets should include data tables, scatter plots with labeled axes, best fit graphs, and equations.

Please perform the following tasks for each of the scenarios 1, 2, 3, 4, and 8.

  1. Create a spreadsheet file, and name it “Track A Part One_Last Name_First Name” (e.g., Track A Part One_Roberts_Mike). Rename the sheet1 as Scenario1.
  2. Insert the data table in the Scenario1 sheet.
  3. Create a scatter plot from the data.
  4. Using the scatter plot, determine the polynomial type that should best fit the data.
  5. Fit the polynomial curve decided upon in the previous step, and display the equation in the spreadsheet itself.
  6. Add sheet2 by clicking the plus button, then rename the sheet2 as Scenario2. Repeat the last 4 steps for each scenario.

Part Two

The task for Part 2 asks students to model equations based on the descriptions/from concepts in scenarios 5, 6, and 9. Download the “Assessment Form” below. Name your file “Track A Part Two_Last Name_First Name” (e.g., Track A Part Two_Roberts_Mike).

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