Question

Summer is thinking about buying a car for $45,000. The table below shows the projected value of two different cars for three years.

Number of years 1 2 3
Car 1 (value in dollars) 40,500 36,450 32,805
Car 2 (value in dollars) 42,000 39,000 36,000

Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

Part C: Summer wants to purchase a car that would have the greatest value in 13 years. Will there be any significant difference in the value of either car after 13 years? Explain your answer, and show the value of each car after 13 years. (4 points)

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

given values for two cars over three years, solve using this information Explanation:

1. first car's value over a few years can be given as a linear function and  depending upon the previous years' value as difference between consecutive year's value is $\frac{1}{10} ^{th$ of previous year's value
2. for first car let current year rate be denoted by $y_x$ , previous year rate be denoted by $y_{x-1$  and $y_1=40500$, then the value of car after a 'x' years is given by, $f_1(x)=y_x= y_{x-1+\frac{y_{x-1}}{10}\ \ \ \ \ \ \ (given\ x\geq 2)$      
3. for second car the value over a few years is also a linear function.
4. for second car the value is getting uniformly decreased by a fixed amount of $3000$ and $y_1=42000$ , then value of car after 'x' years is given by,   $f_2(x)=42000-3000x\ \ \ \ \ \ \ \ (given\ x\geq 2)$    
5. from above functions we get value of each car after $13$ years is ,                                                   $f_1(13)=11,438.4$          $f_2(13)= 3000$          ---(a)
6. summer should purchase first car after $13$ years
7. yes, there is quite significant change in the value of both the cars as given in (a).