Suppose a city with population 300,000 has been growing at a rate of \( 2 \% \) per year. If this rate continues, find the population of this city in 24 years. The population in 24 years will be approximately \( \square \). (Round to the nearest whole number as needed.)

To find the population in 24 years, you can use the formula for exponential growth: \[ P = P_0 (1 + r)^t \] where \( P_0 \) is the initial population, \( r \) is the growth rate, and \( t \) is the time in years. Here, \( P_0 = 300,000 \), \( r = 0.02 \), and \( t = 24 \). Calculating it, we have: \[ P = 300,000 (1 + 0.02)^{24} = 300,000 (1.02)^{24} \] Now, calculate \( (1.02)^{24} \): \[ (1.02)^{24} \approx 1.60844 \] So the population in 24 years will be: \[ P \approx 300,000 \times 1.60844 \approx 482,532 \] Thus, the population in 24 years will be approximately \( 482,532 \). --- Now, to spice things up a bit: The concept of exponential growth is not just confined to populations; it’s also seen in finance with compound interest. For instance, if you invest $100 at an interest rate of 5% compounded annually, in 24 years, your investment would balloon significantly, demonstrating just how powerful compounding can be. To avoid any math mistakes while calculating exponential growth, always make sure to double-check your growth factor. It's easy to confuse the decimal point in growth rates (like 2% vs. 20%) which can lead to wildly inaccurate predictions. Also, remember exponent rules; a little slip here could lead to a big discrepancy down the line!