Question

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

Explanation:

Step1: Identify initial value for a

The initial population is the starting number of birds, which is the value of $a$ in $f(x)=ab^x$.
$a = 240$

Step2: Calculate growth factor for b

For annual growth, $b = 1 + \text{growth rate}$. Convert 16% to decimal: $0.16$.
$b = 1 + 0.16 = 1.16$

Answer:

$a = 240$
$b = 1.16$