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Question 1.d (1 mark) The value of Alex's van could also be depreciated using the reducing balance method of depreciation. The value of the van, in dollars, after \( n \) years, \( R_{n} \), can be modelled by the recurrence relation show below. \[ R_{0}=75000, R_{n+1}=0.943 R_{n} \] At what annual percentage rate is the value of the van depreciating each year? Write your answer... Status: unsaved Question 2 Marlon plays guitar in a band. She paid \( \$ 3264 \) for a new guitar. The value of Marlon's guitar will be depreciated by a fixed amount for each concert that she plays. After 25 concerts, the value of the guitar will have decreased by \( \$ 200 \). Question 2.a (1 mark) What will be the value of Marlon's guitar after 25 concerts? Write your answer... Status: unsaved Question 2.b (1 mark) Write a calculation that shows that the value of Marlon's guitar will depreciate by \( \$ 8 \) per concert. Write your answer...

Ask by Tyler Li. in Australia
Mar 15,2025

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**Question 1.d:** The van depreciates at an annual rate of 5.7%. **Question 2.a:** After 25 concerts, Marlon's guitar will be worth \$3,064. **Question 2.b:** The guitar depreciates by \$8 each concert.

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The annual percentage rate of depreciation for Alex's van can be calculated by recognizing that the recurrence relation uses a factor of 0.943. To find the rate, subtract this factor from 1 and multiply by 100. So, \( (1 - 0.943) \times 100 = 5.7\% \). Therefore, the van depreciates at an annual rate of approximately 5.7%. To find the value of Marlon's guitar after 25 concerts, you start with the original value of \$3264 and subtract the total depreciation. Since the guitar loses \$200 in value after 25 concerts, you compute: \( 3264 - 200 = 3064 \). Thus, the value of Marlon's guitar after 25 concerts will be \$3064.

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