00:01
In this question, they say that the population p in thousands of a particular county from 1971 through 2014 can be modeled by p equals 71 .5 e to the power of 0 .0319t, where t represents the year with t equals 1 corresponding to 1971.
00:19
We're going to use the model to complete the table, rounding our answers to the nearest whole number.
00:23
So i'm going to go to my calculator and in y equals, we have 71 times e to the power of 0 .0319t.
00:37
Now if t equals 1 that corresponded to 1971, 1980 would be time 10.
00:44
So we would evaluate that function y1 at time 10.
00:50
And i'm getting 97 ,678.
00:54
So 97 ,678.
00:57
1990 is time 20.
01:01
So now i want alpha trace that function y1 at time 20.
01:08
I'm getting 134 ,381.
01:11
I'm getting 134 ,381.
01:17
2000 would correspond to time 30.
01:20
So we have alpha trace y1 at 30.
01:25
And i have 184 ,875.
01:31
184 ,875.
01:36
And then 2010, that is time 40.
01:41
So alpha trace y1 at time 40 gives us 254 ,342.
01:51
254 ,342.
01:55
And then in part b, we say according to the model, when will the population of the county reach 360 ,000? so now i'm setting my population p equal to 360.
02:10
This equals 71 .5 times e to the power of 0 .0319t...