Solving 0.9^N = N / 36

May 2010
3
0
Hi,

Can anyone help me figure out how to re-arrange 0.9^N = N /36 to get the value of N?

I'm driving myself nuts trying to remember my high school maths.

Many thanks,

Nick
 

simplependulum

MHF Hall of Honor
Jan 2009
715
427
Wow , it is very difficult to solve by our hands ! By using my calculator , i got \(\displaystyle N \approx 11.13621076\)
 
May 2010
3
0
D'oh! I just realised I put the initial formula in slightly wrong, it should be 1 - 0.9^N = N/36.

Is it not possible to easily re-arrange this?

Thanks

Nick
 
May 2010
3
0
Thanks - I didn't even notice that N = 0 would be a solution!

The equation has come up as I posed a question to myself asking after how many months a reducing balance depreciation methodology (accounting related) would have depreciated a piece of equipment as much as a straight line depreciation methodology.

It has another solution where N > 0 that is approximately 35.1 (found by using a spreadsheet), which is the solution I was aiming to explain by re-arranging the equation.

I'm quite glad it wasn't just a simple re-arrangement and that I'm (hopefully) not missing a basic trick!

Nick