00:01
Hi, here we have the following problem.
00:03
We are told that the value of a computer, t years after purchase, is given by v of t equals 1 ,000 e to the minus 0 .25t.
00:12
At what rate is the computer's value falling after three years? now, the value of the computer is falling.
00:21
Why? because this function over here, e to the minus 025t, is actually a decreasing function.
00:28
The graph of such a function is going to look something like this, where here we have 1 ,000, this is for t equal to 0.
00:39
This is t and this is v of t.
00:41
So you see as time goes by, the value of the computer goes down.
00:47
Okay, of course it makes economic sense, but it's also important to understand this mathematically as well.
00:56
So that's why in order to find the rate at which the computer's value is falling after three years, what we need to do is we need to calculate, we need to find the derivative of the value of the function at 4t equals 3...