e sticker price of a specific model car has been rising at a constant rate of $3
ID: 3116487 • Letter: E
Question
e sticker price of a specific model car has been rising at a constant rate of $350 per year siceits initial year of manufacture (which was 1985, and we will refer to asx-0). After 4 years, the sticker price had risen to $21,450. 3. Th a) Use the last sentence to create an ordered pair of data. b) What was the sticker price of the car in its initial year of manufacture? Write the equation that gives the sticker price of the car y, after x years since the initial year of manufacture. e) d) Assuming this trend continues, when (how many years after 1985) did the car have a sticker price of $22,500? 4. Tuition for a semester at a local college includes a fixed charge for fees plus $195 per credit. This semester, a student is taking 8 credits and her tuition is $1835. a) Define an input variable for this situation, and explain what it represents. b) Define an output variable for this situation, and explain what it represents. e) Write the information in the last sentence as an ordered pair. d) What is the slope, and what does it mean for this situation? e) Write an equation of the line that models this situation. f What is the fixed charge for fees each semester?Explanation / Answer
3(a). The ordered pair, as per the last sentence is (4,21450).
(b). The sticker price of the car has been rising at a constant rate of $ 350 per year so that the price rise in 4 years is 4*350 = $ 1400. Further, since the price of the car, 4 years after the initial year is $ 21450, hence the sticker price of the car in the initial year of manufacture is $ 21450-$ 1400 = $ 20050.
(c ). The equation that gives the sticker price of the car x years after the initial year of manufacture is y = 20050+350x.
(d). Let us assume that the sticker price of the car will be $ 22500, x years after the initial year of manufacture. Then, we have 22500 = 20050+350x or, 350x = 22500-20050 = 2450. Hence x = 2450/350 = 7. Thus, the sticker price of the car will be $ 22500, 7 years after the initial year of manufacture.
4. (a). The input variable(x) for the given situation is the number of credits that a student takes.
(b). The output variable(y) is the total tuition fee per semester at the local college including the fixed charge and the charges for the credits that a student takes.
(c ). The ordered pair as per the last sentence is (8,1835).
(d). The slope is 195. It represents the charge per credit taken from a student.
(e ). The equation of a line that models this situation is y = 195x +c, where c is the fixed charge, x is the number of credits that a student takes and y is the total tuition fee per semester at the local college.
(f). The total tuition fee for a student taking 8 credits is $ 1835 so that 1835= 8*195 +c = 1560+c . Hence c = 1835-1560 = $ 275. Thus, the fixed charge is $ 275.
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