# Delia purchased a new car for $25,350. This make and model straight line depreciated to zero after 13 years. Determine the slope of the depreciation equation. Question Functions asked 2021-03-07 Delia purchased a new car for$25,350. This make and model straight line depreciated to zero after 13 years. Determine the slope of the depreciation equation. 2021-03-08
Let x be the number of years since the car was purchased and y be the value of the car.
Two points representing the situation are (0,25350) when it is purchased as a new car and (13,0) when it depreciated to 0 after 13 years. Using the slope formula, $$\displaystyle{m}=\frac{{{y}{2}-{y}{1}}}{{{x}{2}-{x}{1}}}=\frac{{{0}-{25350}}}{{{13}-{0}}}=-{1950}$$.
The slope is -1950 which means that the value of the car depreciates at a rate of $1950 per year. ### Relevant Questions asked 2021-03-02 Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth$25,000, and its value decreases by 15% each year, 6 years. Finance bonds/dividends/loans exercises, need help or formulas
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You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt. Anthony is working for an engineering company that is building a Ferris wheel to be used at county fairs. He wants to create an algebraic model that describes the height of a rider on the wheel in terms of time. He knows that the diameter of the wheel will be 90 feet and that the axle will be built to stand 55 feet off the ground. He also knows they plan to set the wheel to make one rotation every 60 seconds. Write at least two equations that model the height of a rider in terms of t, seconds on the ride, assuming that when t = 0, the rider is at his or her lowest possible height. Explain why both equations are accurate.
Part 2:One of Anthony's co-workers says, "Sine and cosine are basically the same thing." Anthony is not so sure, and can see things either way. Provide one piece of evidence that would confirm the co-worker's point of view. Provide one piece of evidence that would refute it. Hint: It may be helpful to consider the domain and range of different functions, as well as the relationship of each of these functions to triangles in the unit circle What is the slope of a line perpendicular to the line whose equation is x - y = 5. Fully reduce your answer. What is the slope of a line perpendicular to the line whose equation is x - 3y = -18. Fully reduce your answer. Using the health records of ever student at a high school, the school nurse created a scatterplot relating $$\displaystyle{y}=\ \text{height (in centimeters) to}\ {x}=\ \text{age (in years).}$$
$$\displaystyle\text{After verifying that the conditions for the regression model were met, the nurse calculated the equation of the population regression line to be}\ \mu_{{{0}}}={105}\ +\ {4.2}{x}\ \text{with}\ \sigma={7}\ {c}{m}.$$ About what percent of 15-year-old students at this school are taller than 180 cm? Using the health records of ever student at a high school, the school nurse created a scatterplot relating y = height (in centimeters) to x = age (in years).
After verifying that the conditions for the regression model were met, the nurse calculated the equation of the population regression line to be $$\displaystyle\mu_{{0}}={105}+{4.2}{x}{w}{i}{t}{h}\sigma={7}{c}{m}$$.
About what percent of 15-year-old students at this school are taller than 180 cm? The population of a town increases according to the model $$\displaystyle{P}{\left({t}\right)}={2500}{e}^{{0.0293}}{t}$$, where t is the time in years, with t=0 corresponding to 1990. Use the modek to estimate the population in (a) 2000 and (b) 2010. Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.
1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?
2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?
3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
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6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase? 