00:01
We're asked to answer a question about depreciation of equipment using exponential and logarithmic functions in differentiation of logarithmic functions.
00:12
So we're told for assets such as machines whose market values drop rapidly in the early years of usage.
00:19
Businesses often use the double declining balance method.
00:23
So in practice, a business firm normally employs the double declining balance method for depreciating these assets for a certain number of years, and then switches over to the linear method, which was introduced in a previous exercise.
00:37
The double declining balance formula is given by v of little n equals c times 1 minus 2 over big n to the little n, where c is the initial value of the assets in dollars.
00:56
V of n denotes the book value of the assets at the end of little n years, and big n is the number of years of which the asset is to pre -year.
01:08
In part a, we're asked to find v prime of n.
01:19
Well, we'll use the hint that we'll take the natural log of both sides.
01:30
So the natural log of v of little n equals the natural log of c times 1 minus 2 over big n to the little n.
01:48
And we can use log properties to rewrite this as the natural log of of big v of little n equals the natural log of c plus the natural log, sorry, little n times the natural log of 1 minus 2 over big n.
02:04
Now in this form you can use implicit differentiation to differentiate with respect to little n...