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(0.03)^x\\)\\(f(x) = 1,200(0.97)^x\\)\\(f(x) = 1,200(1.03)^x\\)

Explanation:

Step1: Recall decay function form

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

Step2: Identify given values

Initial population $P=1200$, decay rate $r=0.03$.

Step3: Calculate decay factor

$1-r = 1-0.03 = 0.97$

Step4: Substitute into function

$f(x) = 1200(0.97)^x$

Answer:

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