Answer
a) $\frac{d}{dt}p(t) = 10.12$ thousand/year
b) 1310.97 thousand
c) 10.12 thousand/year
Work Step by Step
First, we need to keep in mind that t is the number of years SINCE 2000.
a)Differentiating p(t) gives us 10.12.
b)In this question t is found by 2010-2000=10, substituting this into the population equation, p(t), gives us:
p(10)=10.12(10)+1209.77 thousand
p(10)= 1310.97 thousand.
c) The population equation shows us a linear equation, so the rate of population growth a year will always be 10.12 as shown in part a).
