Question

when initially observed, a jellyfish population is 240. the population of jellyfish grows exponentially at a rate of 14% each year. write an exponential growth function to model the jellyfish population. let ( f(x) ) represent the number of jellyfish in the population after ( x ) years since the jellyfish population was initially observed. enter your answer in the box. ( f(x) = square )

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth function is $f(x) = a(1+r)^x$, where $a$ is the initial amount, $r$ is the growth rate, and $x$ is time in years.

Step2: Identify given values

Initial population $a=240$, growth rate $r=14\%=0.14$.

Step3: Substitute values into formula

Substitute $a=240$ and $r=0.14$ into the formula:
$f(x) = 240(1+0.14)^x = 240(1.14)^x$

Answer:

$f(x)=240(1.14)^x$