Question

3. The function 𝑝(𝑡) = −50 + (30(11t+13))/2+3t
describes the population, in thousands, of a town t years since
1990.
a) What is the initial population of the town in the year 1990?
b) What is the population of the town in the year 2002?
c) What will the population of the town be eventually?
d) Is the population increasing or decreasing over time? Justify your answer.

Answer 1

I suspect a typo of some sort, since that complicated-looking expression simplifies to just
p(t) = 168t + 145
Aha. You probably meant
p(t) = −50 + (30(11t+13))/(2+3t) = (180t+290)/(3t+2)
since (c) asks about end behavior. See what a difference proper use of parentheses makes? In any case,
(a) p(0) = 290/2 = ___
(b) p(2002-1990) = p(12) = (180*12+290)/(3*12+2) = ____
(c) the horizontal asymptote is at p(t) = 180/3 = ___
(d) compare (a) to (b) to see what's happening