Question

8 the bear population increases at a rate of 2% each year. there are 1573 bears this year. which function models the bear population?
options:
$y = 1605(0.98)^x$
$y = 1573(1.02)^x$
$y = 1605(1.02)^x$
$y = 1573(0.98)^x$

Explanation:

Step1: Recall exponential growth formula

The formula for exponential growth is $y = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the growth rate (as a decimal), and $x$ is the time.

Step2: Identify values

Here, the initial number of bears $a = 1573$, and the growth rate $r = 2\% = 0.02$.

Step3: Substitute into formula

Substituting these values into the formula, we get $y = 1573(1 + 0.02)^x = 1573(1.02)^x$.

Answer:

$y = 1573(1.02)^x$ (the third option, assuming the third option is $y = 1573(1.02)^x$ from the visible text)