Subjects exponential growth

Building Value

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Building Value


1. **State the problem:** We want to find the value of a building at the end of 2010 given that its value increases by 3% each year. The initial value at the beginning of 2004 is 45000 Omani rials. 2. **Understand the growth:** Each year, the building's value increases by 3%, so it is multiplied by $1.03$. 3. **Calculate the number of years:** From the beginning of 2004 to the end of 2010 is 7 years (2004 to 2010 inclusive). 4. **Apply the growth formula:** $$\text{Value at end of 2010} = 45000 \times (1.03)^7$$ 5. **Calculate:** $$ (1.03)^7 = 1.03 \times 1.03 \times 1.03 \times 1.03 \times 1.03 \times 1.03 \times 1.03 \approx 1.22504$$ 6. **Final value:** $$45000 \times 1.22504 \approx 55126.8$$ 7. **Round to nearest 100:** $$55126.8 \approx 55100$$ **Answer:** The estimated value of the building at the end of 2010 is 55100 Omani rials.