1. **State the problem:** A machine costs 45000 and has a salvage value of 4350 after 6 years. The depreciation is computed using a constant percentage rate on the declining book value each year. We need to find the annual rate of depreciation in percentage. 2. **Formula used:** The value after $n$ years with a constant depreciation rate $r$ is given by the formula for exponential decay: $$V_n = P(1 - r)^n$$ where: - $V_n$ is the value after $n$ years, - $P$ is the initial cost, - $r$ is the annual depreciation rate (as a decimal), - $n$ is the number of years. 3. **Apply the known values:** $$4350 = 45000(1 - r)^6$$ 4. **Isolate $(1 - r)^6$:** $$\frac{4350}{45000} = (1 - r)^6$$ $$\frac{\cancel{4350}}{\cancel{45000}} = (1 - r)^6$$ Simplify the fraction: $$\frac{4350}{45000} = 0.0966667$$ 5. **Take the sixth root of both sides to solve for $1 - r$:** $$1 - r = \sqrt[6]{0.0966667}$$ 6. **Calculate the sixth root:** $$1 - r \approx 0.6987$$ 7. **Solve for $r$:** $$r = 1 - 0.6987 = 0.3013$$ 8. **Convert to percentage:** $$r = 0.3013 \times 100 = 30.13\%$$ **Final answer:** The annual rate of depreciation is approximately **30.13%**.