Question

ginny is studying a population of frogs. she determines that the population is decreasing at an average rate of 3% per year. when she began her study, the frog population was estimated at 1,200. which function represents the frog population after $x$ years?
$f(x)=1,200(1.03)^x$
$f(x)=1,200(0.03)^x$
$f(x)=1,200(0.97x)$
$f(x)=1,200(0.97)^x$

Explanation:

Step1: Identify decay rate factor

Since the population decreases by 3% annually, the remaining proportion each year is $1 - 0.03 = 0.97$.

Step2: Use exponential decay formula

The general exponential decay formula is $f(x) = P(1-r)^x$, where $P=1200$ (initial population), $r=0.03$ (decay rate), so substitute values:
$f(x) = 1200(0.97)^x$

Step3: Match to options

Compare the derived function to the given choices.

Answer:

$f(x) = 1,200(0.97)^x$