A population of 240 birds increases at a rate of \( 16 \% \) annually. Jemel writes an exponential function of the form \( f(x)= \) \( a b^{x} \) to represent the number of birds after \( x \) years. Which values should she use for \( a \) and \( b \) ? \( a=\square \) \( b=\square \)

Jemel can set \( a \) as the initial population of birds, which is 240. So, \( a = 240 \). For the growth factor \( b \), since the population increases by \( 16\% \), you convert that percentage to a decimal and add 1. Thus, \( b = 1 + 0.16 = 1.16 \). So the function would be \( f(x) = 240 \cdot (1.16)^x \). Now, if Jemel wants to project this population accurately over the years, she should also consider factors that might influence the birds’ growth rate, such as food supply and habitat changes. Gathering data on such variables can provide a more realistic model and inform future conservation efforts. When working with exponential functions, common mistakes include forgetting to convert the growth percentage into a decimal or misplacing the initial value. Always double-check that you're working with the right values right from the start to avoid those pesky errors that can lead to wildly inaccurate predictions!