00:01
Alright, so in this problem we're given this function, it's supposed to tell the population in a town from 2010 to 2019 or 2020 or something like that, based on what year it's in.
00:12
So the function is p of t equals 35 .08e raised to the 0 .57t power.
00:20
We want to find what the instantaneous rate of change is in 2016.
00:24
So i put over here, 2010 represents t equals 0, so that means 2016, t will equal 6.
00:33
So we're going to have to plug 6 in.
00:35
To do this we've got to take the derivative, so p prime of t, the derivative is just 35 .08e to the 0 .57t, which is exactly what it's supposed to come out to be.
00:51
Then you take all of this times the derivative of the exponent, which is just 0 .57.
00:58
So there's our function, and now we've just got to plug 6 in for t, and you could multiply 35 .08 times the 0 .57 to make the numbers a little smaller and then plug it in, you don't have to...