00:01
We're told that based on observations, the speed of a jogger can be approximated by v equals 7 .5 times 1 minus 0 .04x to the 3 tenths power.
00:14
So what we're basically saying here is as they go further, their speed goes down because as they go further, they get tired and they can run slower.
00:26
And this is given in miles per hour.
00:31
And so the first thing we're asked for is the distance the jogger has run in one hour.
00:38
So we know that dv dvd t equals the x d t so we can separate variables and we get the integral from zero to the distance they've traveled.
00:50
The x over v as a function of x equals zero to one hour.
00:56
Dt.
00:58
If we do those integrals and some simplification, we can get that one minus 0 .04x prime to the seven tenths power equals 0 .8.
01:12
And we see that they have run 7 .15 miles.
01:18
So we can see that if they hadn't been slowing down, they have been, they would have run 7 .5 miles.
01:22
So we can see that if they hadn't been slowing down, they have been, they would have run 7 .5 miles.
01:26
So, because they're slowing down as they get tired, they run a shorter distance...