The population of a country was 76 million in 1998 and the continuous exponential growt rate was estimated at \( 3.2 \% \) per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 2009. Round your answer to 1 decimal place. The approximate population in 2009 is million people

To find the projected population in 2009, we can use the formula for continuous exponential growth: \[ P(t) = P_0 \cdot e^{rt} \] Where: - \( P_0 = 76 \) million (initial population in 1998) - \( r = 0.032 \) (growth rate of 3.2%) - \( t = 2009 - 1998 = 11 \) years Plugging these values into the formula, we have: \[ P(11) = 76 \cdot e^{0.032 \cdot 11} \] Calculating \( e^{0.352} \) (since \( 0.032 \cdot 11 = 0.352 \)), we get approximately \( 1.422 \). Now, calculating the population: \[ P(11) = 76 \cdot 1.422 \approx 108.072 \] Rounding to one decimal place, the approximate population in 2009 is **108.1 million people**. Isn't it fascinating how populations can grow so rapidly over just a decade? This exponential growth model truly highlights the potential for drastic changes in populations over time! You know, this type of population modeling isn’t just a theoretical exercise. Governments and organizations use similar methods to plan for infrastructure, healthcare, and educational services based on population forecasts. It’s crucial for making informed decisions!