Lesson Objective: Go over the Car Project calculations and format. Date: Car Project Notes   Lesson Objective: Go over the Car Project calculations and format. CCSS: F.IF.4, A.SSE.3, A.CED.4, F.IF.8b You will need: a graphing utility

Lesson 1: Find 3 Cars to Choose From Options BMW 440i $66,950 29 mpg Audi A7 $83,925 Tesla Model S $81,700 mpg N/A 1. Price 3 1 2 2. Fuel Economy 3. Style 4. 5. 6. TOTAL

Lesson 1: Find 3 Cars to Choose From

Lesson 1: Find 3 Cars to Choose From

Lesson 2: Purchase Price, Down Payment and Loan Principal For info on down payment and loan balance/ principal, see 3.1 in the book. List Price: $83,925.00 Est. Reg. Fees @ 5%: 4,196.25 Sales Tax @ 8.75%: + 7,343.44 Purchase Price: $95,446.69 Less 20% Down Payment: - 19,092.94 Loan Principal: $76,353.75

Lesson 3: Find a Loan

Lesson 4: Determine Length of Loan See section 3.4 in the book. t = 𝐥𝐨𝐠 𝑴 𝑷 − 𝐥𝐨𝐠 𝑴 𝑷 − 𝒓 𝟏𝟐 𝟏𝟐𝐥𝐨𝐠 𝟏+ 𝒓 𝟏𝟐 Loan Principal: $76,353.75 Monthly Payment: $250 Interest Rates: 2.95%, 4.72%, 7.15%

Lesson 5: Monthly Payment See section 3.2 in the book. M = 𝑷 𝒓 𝟏𝟐 𝟏 + 𝒓 𝟏𝟐 𝟏𝟐𝒕 𝟏 + 𝒓 𝟏𝟐 𝟏𝟐𝒕 − 𝟏 M = 76,353.75 .𝟎𝟒𝟗𝟓 𝟏𝟐 𝟏 + .𝟎𝟒𝟗𝟓 𝟏𝟐 𝟏𝟐·𝟓 𝟏 + .𝟎𝟒𝟗𝟓 𝟏𝟐 𝟏𝟐·𝟓 − 𝟏 = $1,439.14 You also need to do the calculations for 3 years and 6 years. Find total interest for each one. Choose which term of loan you want to use.

Lesson 6: Expense Function See section 4.5 in the book. y = mx + b m = annual loan payments b = down payment y = 17269.69x + 19092.94

Lesson 7: Depreciation Functions Straight-Line Depreciation: See section 4.5 in the book. y = mx + b m = slope = annual straight-line depreciation b = purchase price (0, 95446.69), (10, 0) y = -9544.67x + 95446.69

Lesson 7: Depreciation Functions Exponential Depreciation: See section 4.6 in the book. y = A(1 – r)x y = 95446.69(1 – .15)x

Lesson 8: Graph

Lesson 8: Graph

Lesson 8: Graph

Lesson 9: Point of Intersection See sections 4.5 and 4.6 Notes. Set your expense function equal to your straight-line depreciation function and solve for x. This should equal the x in the point of intersection between the expense function and the straight-line depreciation function. Plug in x into each function to find the value of y. The y values should be equal and should equal the point of intersection.

Lesson 9: Point of Intersection See sections 4.5 and 4.6 Notes. Plug in the x value of the point of intersection between the expense function and the exponential depreciation function into EACH function and solve for y. The y values should be equal and should equal the point of intersection.

Lesson 10: Interpret the Graph See sections 4.5 and 4.6 Notes and in the book.

Lesson 11: How Long? See section 4.6 Example 6 CYU. Straight-Line Depreciation: y = -9544.67x + 95446.69 ¼ Value = (.25)(95446.69) = 23236.74 = y Plug in y and solve for x.

Lesson 11: How Long? See section 4.6 Example 6 CYU. Exponential Depreciation: y = 95446.69(1 – .15)x ¼ Value = (.25)(95446.69) = 23236.74 = y 23236.74 95446.69 = (1 – .15)x log 23236.74 95446.69 = x log(1 – .15) x =

Lesson 12: What Rate? See section 4.6 Example 7 and CYU in the Notes and in the book. Use rational exponent 𝟏 𝟕 to get rid of the exponent and solve for r.

Lesson 13: What Value? Find the value of y. y = -9544.67x + 95446.69 y = 95446.69(1 – .15)x

Lesson 14: Vacation Time! See section 4.7 Notes and in the book. My destination point: Winnepeg, Manitoba, Canada Mileage (per Google Maps): One Way =1,910.7 mi.; Round Trip = 3,821.4 Average Speed: 65 mph MPG: 29 mpg

Lesson 15: Foreign Soil See section 4.7 Notes and in the book. Use the conversion factor 1 km ≈ 0.621371 mi. 62 km 1000 km 580 km

Lesson 16: Foreign Souvenirs Be sure to make a list of items you will need cash for on your trip. See section 4.7 Notes and in the book. Spending Money Budget: Food: Souvenirs: Entrance Fees: ____________: Total: