Question A town has a population of 12000 and grows at \( 2 \% \) every year. To the nearest year, how long will it be until the population will reach 16200 ?

To solve this problem, we can use the formula for exponential growth, which is \( P(t) = P_0(1 + r)^t \), where \( P(t) \) is the future population, \( P_0 \) is the initial population, \( r \) is the growth rate, and \( t \) is the time in years. Given: - \( P_0 = 12000 \) - \( P(t) = 16200 \) - \( r = 0.02 \) We need to find \( t \): \[ 16200 = 12000(1 + 0.02)^t \] Now divide both sides by 12000: \[ \frac{16200}{12000} = (1.02)^t \] \[ 1.35 = (1.02)^t \] To solve for \( t \), we take the logarithm of both sides: \[ \log(1.35) = t \log(1.02) \] Now solve for \( t \): \[ t = \frac{\log(1.35)}{\log(1.02)} \] Calculating the values: 1. \( \log(1.35) \approx 0.1303 \) 2. \( \log(1.02) \approx 0.0086 \) Thus, \[ t \approx \frac{0.1303}{0.0086} \approx 15.14 \] Rounding to the nearest year, it will take approximately **15 years** for the population to grow from 12,000 to 16,200. Now, about population growth trends: did you know that many cities around the world are experiencing similar growth rates? As urbanization increases, these trends can lead to significant challenges and opportunities in planning resources and infrastructure! And speaking of planning, remember that while a 2% growth might sound small, when compounded over many years, it can lead to surprisingly big changes. So always tune in to the power of percentages—math isn't just numbers; it's a key to understanding the world around us!