00:01
Okay, so you have an initial population of 500.
00:11
The carrying capacity will use capital k is 16 ,000.
00:17
The number of fish tripled in the first year, so p of 1 is equal to three times p not, which is 510, 1500.
00:30
Okay, so it's going to satisfy a logistic equation.
00:34
You need to find an expression for the population and how long will it take it to increase to 5 ,000? so the logistic equation is p of t is equal to k over 1 plus k minus p .0 over p .0 e to the negative k t.
01:06
It says do not round k in your calculations.
01:09
It's easier to find e to the negative k, which is what we're going to do.
01:15
So k is 16 ,000 over 1 plus, 16 ,000 minus 500 divided by 500 is 31.
01:31
So this is 31e to the negative kt.
01:36
P of 1 is 1500.
01:39
So we can say 1500 is equal to 16.
01:44
Thousand over 1 plus 31 e to the negative k notice t will be 1 so 1 plus 31 e to the negative k is equal to 16 ,000 over 1500 we can get rid of two of those zeros 160 divided by 15 is a repeating decimal so we're going to leave it like that we're going to subtract one from both 116 divided by 15 minus 1 is 29 over 3.
02:24
So 31 e to the negative k.
02:28
What we did is 160 minus 15 minus 15 16 over 15 is 1445 over 15 and that reduces to 29 over 3.
02:44
Divide both sides by 31 and you get 29 over 93...