Question 1143282
<br>
{{{P(t) = (200+40t)/(1+0.05t)}}}<br>
{{{graph(400,400,-4,24,-50,600,(200+40x)/(1+0.05x),500)}}}<br>
1. Time for the population to reach 500:  Solve the equation P(t) = 500<br>
{{{(200+40t)/(1+0.05t)=500}}}<br>
2. Average rate of change of the population from year 4 to year 12:  That's the slope of the line passing through (4,P(4)) and (12,P(12)).<br>
{{{(P(12)-P(4))/(12-4)}}}<br>
Both parts of the problem can be worked with pencil and paper; but a graphing calculator makes it much easier....