1. For this first example, the linear equations are greatly simplified versions of the situation, but even the simplified versions can help guide practical decision making. a. You are considering buying a used car for $19,000, because a relative won the lottery and has decided to share with the entire family. You have researched the car thoroughly and have estimated that it will depreciate by $1,850 each year. i. Write an algebraic expression of the relationship among the purchase price, the depreciation, and time. ii. Set that expression equal to the worth of the car, W. . How much would the car be worth after 5 years? iv. When will the car be worth $12,000? b. You have calculated that insurance and repairs will cost about $1460 during the first year, and as the car ages, those costs will increase by $220 each year. (Ignore, for now, fuel costs and the effect of mileage on repair costs. Write an algebraic expression of the relationship among the costs during the first year, the expected increase in costs, and time. 1. Set that expression equal to C, the cost to own the car m. After 3 years, how much will it cost to insure and maintain the car? iv. When will the costs total $3,000? Using your graphing calculator, graph the two equations you formed. Remember that you will have to convert your variables to x and y. Choose an appropriate window size. Take a picture of the screen on your calculator and paste it here. d. Find the intersection of the two lines. What are the coordinates at the point of intersection? e. Explain when you think it would be time to buy a new car, if you purchase the one you are considering 2. Two exclusive gyms are offering new membership packages, Apogee Performance Gym is offering a membership for $200 in registration fees and 550 per month. Tidal Works Gym is offering membership for $400 in registration fees, but only $10 per month. a. Write algebraic equations that represent the cost of joining each gym. b. Graph each equation on your calculator, using appropriate window settings. Take a picture and paste it here Use the graph to determine when cost of belonging to either gym is the same d. If you are sure that you will keep going to the gym for at least a year, which gym would cost less 3. Use algebraic techniques to solve answer these questions a. Using the expressions example from number 1, find the time at which it would cost as much per year to insure and maintain the car as it is worth number of months of membership at which the b. Usi the expressions from example number 2, find cost is the same for each gym