This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — 3. Depreciation Rate The formula for depreciation is A = P(1 - r)^n, where A is the final value, P is the initial value, r is the annual rate of depreciation, and n is the number of years. Step 1: Identify the given values. Initial price, P = shs. 800,000 Final price, A = shs. 550,000 Number of years, n = 4 Step 2: Substitute the values into the formula. 550,000 = 800,000(1 - r)^4 Step 3: Isolate (1 - r)^4. (550,000)/(800,000) = (1 - r)^4 (55)/(80) = (1 - r)^4 (11)/(16) = (1 - r)^4 Step 4: Take the fourth root of both sides to solve for (1 - r). 1 - r = ((11)/(16))^(1)/(4) 1 - r = [4]11[4]16 1 - r = [4]112 Calculate [4]11: [4]11 ≈ 1.82115 1 - r ≈ (1.82115)/(2) 1 - r ≈ 0.910575 Step 5: Solve for r. r = 1 - 0.910575 r = 0.089425 Step 6: Express the rate as a percentage. r = 0.089425 × 100\% r ≈ 8.94\% The annual rate of depreciation is 8.94\%. Send me the next one 📸