00:01
So in this problem, we're given this graph of deer population in pennsylvania county between 2010 and 2014.
00:11
And we're asked a series of questions.
00:15
First question is the deer population in 2010.
00:28
Well, that's just this initial value right on the graph, isn't it? and so that means that the answer here is 20 ,000 deer.
00:50
Next question.
00:51
We're asked to find a function that models this deer population t years after 2010.
01:22
Well, we're told that this grows exponentially.
01:30
So by the exponential model then we have n of t the number of deer and t years is the initial value e to the r t okay so we have our initial value so we have this and we have this point right here so we have two points on this curve so we can use those with the formula here to solve for r so that we can then write the model so here we go we know that at twenty thousand we know this sorry about that we know thirty one thousand is twenty thousand the initial amount e to the r and then t is four in it okay so divide both sides by twenty thousand so that gives us thirty over 20 ,000 is equal to e to the 4r.
02:59
Okay.
03:03
These three zeros all cancel out.
03:08
And if i do ln of e to the x, well, the natural log in e cancel each other out, so i just left with that exponent.
03:18
So that means if i take the natural log of both sides, then i have the ln of 31 over 20 equals ln of e to the, 4r which means that equals 4r all right now then divide by four and so i have that r is ln of 31 over 20 times one fourth right or divided by four and this is approximately 0 .196 so n of t is n of t is 20 ,000 e to the 0 .1096t.
04:26
So there is the model that we were asked to find.
04:35
Okay, part c.
04:37
Whereas what's the projected deer population in 2018? well, from 2010, all right, 2018 minus 2010 would be 8.
04:57
So t is eight so this is in of eight equals 20 ,000 e the 0 .1096 times eight and so we multiply this out this is approximately 48 ,000 deer in 2018...