Suppose that today (year 0) your car is worth $17,000. Each year your car loses 10% of its value, but at the end of each year you add customizations to your car which increase its value by $20. Write a recurrence relation to model this situation. C (n) = if n = 0 + · C (n - 1) if n > 0

Question

Oneill

Mathematics

12 November, 03:08

Suppose that today (year 0) your car is worth $17,000. Each year your car loses 10% of its value, but at the end of each year you add customizations to your car which increase its value by $20. Write a recurrence relation to model this situation. C (n) = if n = 0 + · C (n - 1) if n > 0

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Answers (1)

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Darnell Mays · Answer 1

Step-by-step explanation:

since

current value = added value by customisation + remaining value after loosing worth (100%-10% = 90%)

therefore

C (n) = $20 + 0.9*C (n-1) for n>0

C (n) = Co=$17000 for n=0

where

C (n) represents the value of the car at the end of the nth year, C (n-1) is the value at the end of the (n-1) th year and Co is the initial value