Subjects algebra

Price Decline 6C92E3

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1. **State the problem:** We have a product with a current selling price of 325. The price declines by 10% per year due to obsolescence. We want to find the selling price after 4 years. 2. **Formula used:** The price decline is exponential decay, so we use the formula for depreciation: $$ P_t = P_0 \times (1 - r)^t $$ where: - $P_t$ is the price after $t$ years, - $P_0$ is the initial price, - $r$ is the rate of decline per year (as a decimal), - $t$ is the number of years. 3. **Apply the values:** - $P_0 = 325$ - $r = 0.10$ - $t = 4$ 4. **Calculate:** $$ P_4 = 325 \times (1 - 0.10)^4 = 325 \times 0.90^4 $$ 5. **Simplify:** $$ 0.90^4 = 0.90 \times 0.90 \times 0.90 \times 0.90 = 0.6561 $$ 6. **Final price:** $$ P_4 = 325 \times 0.6561 = 213.2325 $$ 7. **Answer:** The selling price after 4 years will be approximately **213.23**.