00:01
For this problem, we want to find the population of a certain bacteria after one hour, given that its population at t equals 0 is 2 ,000, and the rate of growth is given by the expression 1 ,000 times 8 raised a power of t per hour after t hours.
00:21
Then our p of t, which will be the population function, is equal to.
00:30
To the antiderivative of the rate of growth, which is 1 ,000 times 8 raised of power of t d t.
00:40
That's equal to 1 ,000 times 8 raise of power of t all over natural log of 8 and then plus c.
00:52
If the population at t equals 0 is 2 ,000, then p of 0 is equal to 1 ,000 times 1 ,000 times 8 raise of power of 0 over the natural log of 8 plus c, which implies that 2 ,000 equals 1 ,000 over natural log of 8 plus c...