00:01
Okay, so the deer population at 2006 is 80, and it grows to 180 in 2012.
00:10
And so we're asked to write an exponential function.
00:14
So we know that n -t would be something like n at zero times the rate of growth or decay to the power of t, t being years.
00:29
We know that n of 0, that 0 is 80, and n at 6 is 180.
00:36
So let's figure out what r is.
00:39
180 equals 80 times r to the power of 6.
00:46
180 divided by 80 is equal to r to the power of 6.
00:51
And that works out to 2 .25 is equal to r to the power of 6.
00:58
6.
00:58
This is when we bring logarithms in equals 6 times log of r.
01:09
So my log of r is equal to log 2 .25 all over 6.
01:19
So my log of r is equal to 0 .58 and so that means that r would be equal to 10 to the power of 0 .058 and it gives me an r of 1 .147.
01:43
So my exponential function is n of t is equal to 80 times 1 .1447 to the power of t.
02:01
From there, it says use technology to create a graph.
02:05
So i went on to desmos and came up with this graph.
02:11
And so we can see that this point here at 0 is 80, and with a little bit of work we probably could have read at 6.
02:19
But i'm not going to worry about that because i felt it was best to zoom in as best i could, and then use the hovering with desmos to come up with these points, and then i labeled them...