00:01
So in this question, they say that a population of a certain state in thousands from 1995, which is t equals zero to 2005, which is t equals 10, is modeled by the polynomial p of t equals negative 0 .3 t squared plus 112t plus 7349.
00:23
In part a, i want to determine the average growth rate from 1995 to 2005 to 2005.
00:30
So that's from time 0 to time 10.
00:35
So how do i find that average growth rate? well, i'm going to be finding the slope of my secant line connecting the points where t is equal to 0 and t is equal to 10.
00:47
So that my setup is looking like p of 10 minus p of 0 over 10 minus 0.
00:57
And i'm going to head to my calculator in order to do this.
01:00
I'm going to say in y1, let's put in negative 0 .38t squared plus 112t plus 7349.
01:17
And i am computing y1 of 10 minus y1 of 0.
01:30
Dividing this by 10 minus 0, i'm getting 108.
01:35
So i'm getting for part a, 108 .2 ,000 people per year in part b.
01:46
I want the growth rate for the state in 1997, which is time 2, and 2005, which is time 10.
01:54
So to do that, i'm going to need my derivative, p prime of t.
01:59
My p prime of t here is negative 0 .7.
02:04
6t plus 112.
02:08
And so if i want the growth rate in 1997, that's p prime of 2.
02:15
That's negative 0 .76 times 2 plus the 112, giving me 110 .48...