A town's rate of population change is modeled by P'(t) = 34t + 16, where t is numbe

[hgsmith]

A town's rate of population change is modeled by P'(t) = 34t + 16, where t is number of years since 1990 an P'(t) is in people per years.
a) Find the population model for this town if it is known that in 2000, the town had a population of 2500.
b) Forecast the town's population in 2015.

I'm having trouble figuring out where I should begin with this problem. Does anyone have an idea?

 

[ksdhart2]

Well, you're given P'(t) which is the derivative of P(t). So how do you think you might find the original function P(t)? This function will then have an unknown constant of (what?), so you'll need to use the given information about the population in 2000 to determine what that constant is. Finally, part (b) asks you to use the function P(t) to evaluate the function P(t) for the year 2015. If you get stuck trying these steps, that's okay, but please include any efforts you've made anyway, even if you know they're wrong. Thank you.