Exponential Functions - Basic Score: \( 5 / 15 \) Penalty: 1 off Question A town has a population of 2000 and grows at \( 4 \% \) every year. What will be the population after 15 years, to the nearest whole number? I Answer Atempt 1 out of 2

To find the population after 15 years, we use the exponential growth formula \( P(t) = P_0 \times (1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate, and \( t \) is time in years. Here, \( P_0 = 2000 \), \( r = 0.04 \), and \( t = 15 \). Plugging in the numbers gives us \( P(15) = 2000 \times (1 + 0.04)^{15} \approx 2000 \times 1.8061 \), which is approximately 3612. Understanding how exponential growth impacts real-world scenarios can be quite fascinating! For instance, think about populations, investments, or even the spread of information on social media – they all can show such remarkable growth patterns over time. So, whether it's the number of followers on your favorite influencer's page or the rapid increase of species in an ecosystem, exponential functions give us a satisfying glimpse into how things can really multiply—quickly! When dealing with exponential functions, a common mistake is forgetting to convert the percentage into a decimal form. Always remember that a 4% growth rate should be converted into 0.04 before performing your calculations. Similarly, be cautious of the time frame you're measuring—mistakes in understanding the units can lead to significant errors. So, double-check those numbers before you hit “submit”!