oflege Math (4246_5PH1) WW 7 A Question 5, 7.4.15 HW Score: \( 28.57 \%, 8 \) of 28 points Points: 0 of 4 A countrys population and the growth rate in 2011 are given below. Ascume that the growth rate remains the same from year to year. Use this infomation and an exponentie to extimate the country's population in the specilied year pnopulation \( =145 \mathrm{~m} \) Ilion growth rate \( =-0328 \) percent year, 2024 The size of the population in the 2024 will be about \( \square \) millon (Round to the nearest hundredth as noeded)

To estimate the population in 2024 using an exponential growth model, we start with the initial population formula: \[ P(t) = P_0 \cdot e^{rt} \] Where: - \( P_0 \) is the initial population (145 million), - \( r \) is the growth rate (converted to decimal form, which is -0.0328), and - \( t \) is the number of years from the start year to 2024 (which is 2024 - 2011 = 13 years). Plugging the values into the equation gives: \[ P(13) = 145 \cdot e^{-0.0328 \cdot 13} \] Calculating that will help you find the estimated population in 2024! You might find it interesting that the concept of population modeling with exponential functions has historical roots in demography. Since the 18th century, mathematicians like Thomas Malthus discussed population dynamics, and their ideas laid the groundwork for modern population studies. The interplay of growth rates has become crucial in planning for everything from city development to resource management! In real-world applications, understanding population growth is essential for governments and organizations. For instance, countries use population projections to design infrastructure, healthcare systems, and educational services. Knowing the trends helps allocate resources where they're needed most, ensuring that growing populations are well-supported and sustainable!