Subjects algebra

Population Growth A4844C

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1. **State the problem:** A town has a population of 18000 and grows at 2% every year. We want to find the population after 11 years, rounded to the nearest whole number. 2. **Formula used:** The population growth can be modeled by the exponential growth formula: $$ P(t) = P_0 \times (1 + r)^t $$ where: - $P(t)$ is the population after $t$ years, - $P_0$ is the initial population, - $r$ is the growth rate (as a decimal), - $t$ is the number of years. 3. **Identify values:** - $P_0 = 18000$ - $r = 0.02$ (2% growth rate) - $t = 11$ 4. **Calculate:** $$ P(11) = 18000 \times (1 + 0.02)^{11} = 18000 \times 1.02^{11} $$ 5. **Evaluate the power:** $$ 1.02^{11} \approx 1.2434 $$ 6. **Multiply:** $$ P(11) = 18000 \times 1.2434 = 22381.2 $$ 7. **Round to nearest whole number:** $$ \boxed{22381} $$ So, the population after 11 years will be approximately 22381 people.