Question

1. the local rodent population numbers approximately 600 and is increasing at a rate of 8% per year.

2a write a function, $y$, that represents the population after $t$ years.
enter your next step here

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth function is $y = P(1 + r)^t$, where $P$ is the initial population, $r$ is the annual growth rate, and $t$ is time in years.

Step2: Identify given values

Initial population $P = 600$, growth rate $r = 0.08$ (8% converted to decimal).

Step3: Substitute values into formula

Substitute $P=600$ and $r=0.08$ into the growth function:
$y = 600(1 + 0.08)^t$

Step4: Simplify the expression

Simplify $1 + 0.08 = 1.08$, so the function becomes:
$y = 600(1.08)^t$

Answer:

$y = 600(1.08)^t$