Question

algebra 1b - standard (15261)
ential decay functions
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: Recall decay function form

The general exponential decay function is $f(x) = P(1-r)^x$, where $P$ is initial population, $r$ is decay rate, $x$ is time.

Step2: Identify given values

$P=1200$, $r=0.03$. Calculate the decay factor:
$1-r = 1-0.03 = 0.97$

Step3: Substitute into function

Substitute $P$ and decay factor into the formula:
$f(x) = 1200(0.97)^x$

Step4: Match to options

Compare with the provided options to find the correct function.

Answer:

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