4x Parameters of an Exponential Function Consider the function f(x)=5,200(1.1)^x which models the yearly cottontail rabbit population in Orange County. 4x What does the value 5,200 represent in the function? A growth factor B number of years 4x C growth rate 4x D initial population 4x What does the value 1.1 represent in the function? 4x A growth factor 4x B number of years 4x C growth rate

## Step 1<br />The given function is \(f(x) = 5,200(1.1)^x\). This is an exponential function, which is generally represented in the form \(f(x) = ab^x\), where \(a\) is the initial amount, \(b\) is the growth factor, and \(x\) is the time.<br /><br />## Step 2<br />In the given function, 5,200 is the coefficient of the exponential term. In the context of the problem, this represents the initial population of cottontail rabbits in Orange County. This is because when \(x = 0\) (i.e., at the beginning), the function simplifies to \(f(0) = 5,200(1.1)^0 = 5,200\). This means that the initial population of rabbits is 5,200.<br /><br />## Step 3<br />The base of the exponential term, 1.1, is the growth factor. This means that each year, the rabbit population grows by a factor of 1.1. This is because when \(x = 1\) (i.e., after one year), the function simplifies to \(f(1) = 5,200(1.1)^1 = 5,720\). This means that the rabbit population increases by 10% each year.