**Percentages — formulas used here.** - Definition. $x\%$ means $\tfrac{x}{100}$. - Increase consumption. If price rises by $R\%$ and spending must stay constant, consumption falls by $\tfrac{R}{100+R} \times 100\%$. - Decrease consumption. If price falls by $R\%$ and spending must stay constant, consumption rises by $\tfrac{R}{100-R} \times 100\%$. - Growth. A population $P$ growing at $R\%$ a year becomes $P(1 + \tfrac{R}{100})^n$ after $n$ years, and was $P / (1 + \tfrac{R}{100})^n$, $n$ years ago. - Depreciation. A value $V$ depreciating at $R\%$ a year becomes $V(1 - \tfrac{R}{100})^n$ after $n$ years. - Reciprocal comparisons. If A is $R\%$ more than B, then B is $\tfrac{R}{100+R} \times 100\%$ less than A. If A is $R\%$ less than B, then B is $\tfrac{R}{100-R} \times 100\%$ more than A. **Question.** A town's current population is $50{,}000$ and grows at $10\%$ per year. What was its population $2$ years ago (to the nearest whole number)?