An initial population of 580 quail increases at a rate of \( 17 \% \). It is represented by this formula \( f(t)=580(1.17)^{t} \). What is the population after 3 years?

To find the population of quail after 3 years using the formula \( f(t) = 580(1.17)^{t} \), we plug in \( t = 3 \): \[ f(3) = 580(1.17)^{3} \] Calculating \( (1.17)^{3} \) gives approximately \( 1.6047 \). Now, multiply this result by 580: \[ f(3) \approx 580 \times 1.6047 \approx 930.726 \] Rounding to the nearest whole number, the population after 3 years is approximately 931 quail. To visualize this growth, imagine a small flock of quail doubling gnarly tree branches and laying eggs in the sun. In just a few years, that charming initial group of 580 can almost become a bustling quail community of nearly 931 birds, balancing the picturesque scene in nature with their vibrant chirping! The concept illustrates the power of exponential growth, showcasing how living organisms can thrive under favorable conditions.