00:01
Good day, the topic is about rate of change.
00:04
The rate of change is defined as the change in the quantity with respect to the change in time, and that this can be expressed in terms of a derivative.
00:12
Suppose we have the function that tells us the concentration of drug as a function of time, as 27e to the negative 0 .01t, where f of t is a concentration in nanograms per ml.
00:27
We wish to find the concentration of the drug after four hours, that means f at 4 and also the rate of change at the given time so we start by simply substituting t with 4 in the given function and that solves for the concentration of the drug f at this at time equals 4 so you have 27 e to the negative 0 .01 times 4 doing this in our calculator gives us 27 times 0 .0 0 .9608 then multiply by 27 that gives us 25 .9 nanogram per m l the concentration of the drug at time equals 4 is 25 .9 nanogram per m.
01:27
If given time we wish to find the rate of change.
01:32
So as been said, rate of change can be expressed as a derivative.
01:37
So let's find the derivative, the derivative, the function, the first so you have 27 e to the negative 0 .01d so note that for the derivative of a constant or rather the derivative of e we just need to copy the expression of e and then we take the derivative of its exponent so the derivative of negative 0 .01 t is negative 0 .01 and then we just need to copy that 27 that's multiplied to t so that we have negative 27 times negative 0 .01...