00:01
In this problem, we're told that a small lake is getting stocked with a certain species of fish.
00:04
And this function, p of t, represents the total number of fish in terms of thousands that's in the lake after t years after it's been stopped.
00:12
So in part a, we want to find the population after three years.
00:15
Well, that's our t value.
00:16
So in this case, we just need to substitute three in place of t.
00:20
So i have 14 getting divided by 1 plus 4 times e to the negative 0 .5 t power.
00:26
Or sorry, i forgot we're substituting in three for t.
00:30
So now we can go ahead and type this into our calculator.
00:34
Just remember that your entire denominator has to be in a preemphasy.
00:37
So in this case, we're going to have 14 divided by open parentheses, 1 plus 4, then our constant e raised to the negative 0 .5 times 3 power.
00:47
And don't forget to close the preface.
00:49
And in this case, they want to the rounds in the nearest whole number.
00:51
So you'll find that there would be approximately 7 ,000 fish.
00:55
And it'd be a little bit over that.
00:58
All right.
00:59
Now, in part b, they want us to figure out after how many years will the population reach 7 ,000.
01:03
So in this case, that's our p of t value.
01:07
But remember, p of t is in terms of thousands...