Please check my work and let me know if you think my formulas are correct. Thank you
Maintenance costs include some things that remain constant every year, like oil changes, and others that have a tendency to rise as cars get older. In fact, it's this annual rise in maintenance costs that makes them an essential element in our model. Pause to consider what would happen if the cost of maintaining your car didn't change. Without doing any math, just thinking about it.. maintenance How often should your replace your car if its maintenance costs are the same every year as long as you own it? Explain briefly. Indefinitely , b/ C as long as it runs, the same ( constant amount of If is required to maintain it every year Let's assume that annual maintenance costs rise linearly. That is, they go up by the same amount each year. In fact, let's assume that maintenance costs are $200 the first year, then $400 the second year, $600 the third year, and so on. Complete the table below to determine how much you'll spend each yr year over the first five years of ownership, and also how much total you'll have spent total on maintenance throughout the first year, the first two years, the first three years, the first four years, and the first five years of car ownership. As before, a column is provided for you to write words or expressions that may help you generalize later. Year of How determined? ownership Maintenance cost this year Total maintenance costs up to and including this year. (cumulative costs) $ 200 $ 200 initial cost / in given 2 400 60 0 200 + 400 = 400 3 600 1200 yn z yr 3 600 + 600 = 1200 4 800 2000 200+ 800 5 1000 3,000 2000 + 1000 = 3006 We need to generalize the cumulative maintenance costs as well. Look back at your table on page 3 of this document. Look at the values in the third column and the notes or algebra you wrote in the fourth. Develop an expression that gives the total accumulated costs of maintenance over the first x years of owning your car. Let's call it M (x). M (x ) = 100 x + 10ax How many cars will you own if you drive for 50 years and replace your car every x years? Write a formula for it below. Don't worry if it gives fractional values sometimes. That's normal in mathematical modeling. Number of cars owned = 50 / x Now put it all together. Put together the elements on the previous page and this one to write a mathematical model for the total lifetime cost of car ownership if you replace your car every x years. Let's call it C (x). ? CL= (100x 2 + 100 x ) + (50/x ) 20,000 ( 0. 85 ) C ( x ) = 25,000 - R (x) + m () 25, 000 - 20000 (. 85 ) + 10ox + 100x 200 600 1200 2000 3000 V 800 10 0 0 V Quachatic 200 200 a , = b ( 1 ) 2 + c ( 1 ) + d = 200 6 + c +d = zod a2 : 6 ( 2 ) 2 + 6 ( 2 ) +d : 60d 4 6 + 2 c + 1 = 60 0 a3 = 6 ( 3 ) 2 + [ ( 3 ) + d = 1200 96 + 3 C +1 = 1206
