Determming \( a \) and \( o \) values in an Exponental Growth Scenario 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 \( b \) ? \[ \begin{array}{l} a=\square \\ b=\square \end{array} \]

To model the population growth of the birds using an exponential function of the form \( f(x) = a \cdot b^{x} \), we need to determine the values of \( a \) and \( b \). ### Given: - **Initial Population (\( a \))**: The initial number of birds is **240**. This represents the value of \( a \) in the exponential function. - **Annual Growth Rate**: The population increases by **16%** each year. To incorporate this growth rate into the function, we convert the percentage to a decimal and add it to 1: \[ b = 1 + \text{growth rate} = 1 + 0.16 = 1.16 \] ### Exponential Function: Putting it all together, the exponential function modeling the bird population is: \[ f(x) = 240 \cdot (1.16)^{x} \] ### Values: \[ \begin{array}{l} a = 240 \\ b = 1.16 \end{array} \] **Final Answer:** \[ \begin{array}{l} a = 240 \\ b = 1.16 \end{array} \]