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Question 1162575: . Suppose you own a car that is 40 months old. From an automobile dealer’s “Blue Book” you find that its trade-in value is SR3200. From an old Blue Book you find that its trade-in value 10 months ago was SR4700.
a. Write a function expressing trade-in value as a function of the cars age in months.
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b. You plan to get rid of the car when its trade-in value drops to SR1000. How much longer should you keep the car?
c. What does the slope of your function represent in the real world? Why is it negative?
d. When do you predict that car will be worthless? How do you know this?
e. According to your model, what was the trade-in value of the car when it was new?
f. Graph the function.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation i used is y = mx + b
this is a straight line depreciation equation.
m is the slope
b is the y-intercept
2 points on this equation are known.
they are (30,4700) and (40,3200)
these points are in (x,y) format where x is the number of months and y is he value of the car.
the slope is found by the equation of (y2-y1)/(x2-x1)
assign (30,4700) to (x1,y1) and assign 40,3200 to (x2,y2) and replace those values in the slope equation to get:
(3200 - 4700) / (40 - 30) = -1500 / 10 = -150
m is equal to -150 and the equation the becomes y = -150x + b
to solve for b, replace x and y with one of tghe coordinate points to get:
4700 = -150 * 30 + b
simplify and solve for b to get:
b = 4700 + 4500 = 9200
this makes the equation y = -150 * x + 9200 *****
answers to your questions are shown below:
a. Write a function expressing trade-in value as a function of the cars age in months.
y = -150 * x + 9200
y represents the value of the car and x represents the age of the car in months.
b. You plan to get rid of the car when its trade-in value drops to SR1000. How much longer should you keep the car?
replace y with 1000 in the equation to get:
1000 = -150 * x + 9200
subtract 1000 from both sides of the equation and add 150 * x to both sides of the equation and combine like terms to get:
150 * x = 8200
solve for x to get x = 8200 / 150 = 54.667 months rounded to 3 decimal places.
c. What does the slope of your function represent in the real world? Why is it negative?
the slope indicates that the value of the car is dropping by an average of 150 dollars for each additional month in the age of the car.
the slope is negative because the value of the car is dropping by that amount each month, on average.
d. When do you predict that car will be worthless? How do you know this?
set y = 0 to get 0 = -150 * x + 9200
add 150 * x to both sides of the equation to get:
150 * x = 9200
divide both sides of the equation by 150 and solve for x to get:
x = 9200 / 150 = 61.333 months rounded to 3 decimal places.
e. According to your model, what was the trade-in value of the car when it was new?
based oan the equation, the trade-in value of the car when it was new was 9200.
f. Graph the function.
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