The population of a town P(t)is modelled by the function P(t)=6t^2+110t+3000, where t is time in years. Note t=0 represents the years 2000. When will the population reach 6000?

Question

Damon · Answer

2015 see below

Nina · Answer

yes thank u but i don't understand simplified form please!!

mathgeekdude · Answer

just plug it in. 6t^2+110t+3000=6000, thus 6t^2+110t-3000=0 and we factor but first we divide by 2. Thus we get the equation 2(3t+100)(t-15)=0. FYI if you did not learn what just happened please study your algebra book. Anyway, x= -100/3 or 15, but it cannot be negative so t=15. Thus, 2000+15 = 2015