Question

select the correct answer. in 2010, there were 400 frogs in the lake at a local nature preserve. each year, the population of frogs grows by 10%. which equation accurately describes the population of frogs f(x), x years after 2010? - f(x) = 10(400)^x - f(x) = 400(0.1)^x - f(x) = 400(1.1)^x - f(x) = 0.1(400)^x

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth is $f(x) = P(1 + r)^x$, where $P$ is the initial population, $r$ is the annual growth rate, and $x$ is the number of years.

Step2: Identify given values

Initial population $P = 400$, growth rate $r = 10\% = 0.1$.

Step3: Substitute values into formula

Substitute $P=400$ and $r=0.1$ into the formula:
$f(x) = 400(1 + 0.1)^x = 400(1.1)^x$

Answer:

$f(x) = 400(1.1)^x$