Question

1. the local rodent population numbers approximately 200 and is increasing at a rate of 4% per year. write a function, y, that represents the population after t years.

Explanation:

Step1: Identify the growth model

This is an exponential growth problem. The general 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 the time.

Step2: Determine the values of \(a\) and \(r\)

The initial population \(a = 200\). The growth rate is \(4\% = 0.04\), so \(1 + r=1 + 0.04 = 1.04\).

Step3: Write the function

Substitute \(a = 200\) and \(1 + r = 1.04\) into the exponential growth formula. So the function is \(y = 200(1.04)^t\).

Answer:

\(y = 200(1.04)^t\)