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...

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$$
\textbf{Question 1.d:}
$$

We are given the recurrence:
$$
R_{0}=75000, \quad R_{n+1}=0.943\,R_{n}.
$$
The factor $$0.943$$ means that each year the van retains $$94.3\%$$ of its value. Thus, the annual depreciation rate is:
$$
100\% - 94.3\% = 5.7\%.
$$

$$
\textbf{Question 2.a:}
$$

Marlon paid $$\$3264$$ for the guitar. After 25 concerts the value decreases by $$\$200$$. Therefore, the value of the guitar after 25 concerts is:
$$
3264 - 200 = 3064.
$$
Thus, the value is $$\$3064$$.

$$
\textbf{Question 2.b:}
$$

To find the depreciation per concert, we divide the total depreciation by the number of concerts:
$$
\frac{200}{25} = 8.
$$
Hence, the guitar depreciates by $$\$8$$ per concert.
**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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