# A population problem

• Jun 8th 2008, 11:07 PM
Airjunkie
A population problem
Hi guys, i need help with this problem that i seriously have no idea with.

So:

$C(t)= 100sin(2(3.14)/7(t-3))+200$ with t=0 representing the year 1990.

1. What is the population of elk in the year 2004

2. Determine the years between 1990 and 2020 in which the elk population is at its maximum

3 Explain the period of the function in context of the problem

4 Graph the function showing the elk population from 1990 to 2020. identify the points on the graph you determined in parts 1 and 2.
• Jun 9th 2008, 04:12 AM
topsquark
Quote:

Originally Posted by Airjunkie
Hi guys, i need help with this problem that i seriously have no idea with.

So:

$C(t)= 100sin(2(3.14)/7(t-3))+200$ with t=0 representing the year 1990.
1. What is the population of elk in the year 2004

t = 2004 - 1990 = 14

Quote:

Originally Posted by Airjunkie
2. Determine the years between 1990 and 2020 in which the elk population is at its maximum

Set $C'(t) = 0$ and solve for t.
$C'(t) = 100~cos \left ( \frac{2 \pi}{4(t - 3)} \right ) \cdot -\frac{2 \pi}{7(t - 3)^2}$

I leave part 3 to you and part 4 is trivial.

-Dan