Subjects algebra

Exponential Earnings A42D21

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1. **State the problem:** Mohsin’s earnings increase exponentially at a rate of 8.7% each year. In 2018, he earned 195600. We want to find how much more he earns in 2027 compared to 2018. 2. **Formula used:** The formula for exponential growth is $$A = P(1 + r)^t$$ where: - $A$ is the amount after time $t$ years, - $P$ is the initial amount, - $r$ is the growth rate (as a decimal), - $t$ is the number of years. 3. **Identify values:** - $P = 195600$ - $r = 0.087$ - $t = 2027 - 2018 = 9$ 4. **Calculate earnings in 2027:** $$A = 195600(1 + 0.087)^9 = 195600(1.087)^9$$ 5. **Calculate $(1.087)^9$:** $$1.087^9 \approx 2.039$$ 6. **Calculate $A$:** $$A = 195600 \times 2.039 = 398798.4$$ 7. **Calculate how much more he earns in 2027 than 2018:** $$\text{Difference} = A - P = 398798.4 - 195600 = 203198.4$$ **Final answer:** Mohsin earns approximately 203198.4 more in 2027 than in 2018.