2022-05-11
Belinda is thinking about buying a car for $18,500. 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) | 17,390 | 16,346.60 | 15,365.80 |
Car 2 (value in dollars) | 17,500 | 16,500 | 15,500 |
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: Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years? Explain your answer, and show the value of each car after nine years. (4 points)
nick1337
Expert2022-05-13Added 777 answers
Part A
The function that can be used to describe the value of each of the cars after a fixed number of years is an exponential function. This is because the value is reducing at a constant rate(in percent) each year.
Part B
The formula for determining exponential decay is expressed as
Where
represents the value after years.
represents the initial value.
represents the rate of decay.
For Car ,
The function describing the value after years is
For Car ,
The function describing the value after years is
Part C
If she buys Car for , after years, the value will be.
If she buys Car for , after years, the value will be.
The difference would be
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