Subjects algebra

Laptop Value

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1. **Problem Statement:** A laptop was purchased for RM 3000. Its value decreases each year according to the formula $$3000 \times \left(\frac{9}{10}\right)^n$$ where $n$ is the number of years after purchase. We need to find the value of the laptop after 4 years and round it to the nearest RM. 2. **Formula Used:** The value after $n$ years is given by: $$V = 3000 \times \left(\frac{9}{10}\right)^n$$ This is an example of exponential decay where the value decreases by a factor of $\frac{9}{10}$ each year. 3. **Calculate the value after 4 years:** Substitute $n=4$: $$V = 3000 \times \left(\frac{9}{10}\right)^4$$ 4. **Evaluate the power:** $$\left(\frac{9}{10}\right)^4 = \frac{9^4}{10^4} = \frac{6561}{10000} = 0.6561$$ 5. **Calculate the value:** $$V = 3000 \times 0.6561 = 1968.3$$ 6. **Round to the nearest RM:** The value after 4 years is approximately RM 1968. **Final answer:** $$\boxed{1968}$$