Question

1. the local rodent population numbers approximately 290 and is increasing at a rate of 4% per year. 15a write a function, y, that represents the population after t years. enter your next step here

Explanation:

Step1: Identify the growth model

This is an exponential growth problem. The formula for exponential growth is $y = a(1 + r)^t$, where $a$ is the initial amount, $r$ is the growth rate (in decimal), and $t$ is time.

Step2: Determine the values of a and r

The initial population $a = 290$. The growth rate $r = 4\%= 0.04$.

Step3: Substitute the values into the formula

Substitute $a = 290$ and $r = 0.04$ into the exponential growth formula: $y = 290(1 + 0.04)^t$.
Simplify $1 + 0.04$ to get $1.04$, so the function is $y = 290(1.04)^t$.

Answer:

$y = 290(1.04)^t$