find a general formula for N reductions

**sergeyrar123** · February 2nd 2013, 05:22 AM

Hi,

I want to find what will be left of number X, after 50 reductions of 2% - each time the reference is whats left from the total sum.

I was trying to find a general formula for this but without success.

x - 0.02X - 0.02(x-0.02x) - 0.02(x - 0.02X - 0.02(x-0.02x)) - ..... (N times)

please help me find a formula for N reductions.

**earboth** · February 2nd 2013, 05:44 AM

Originally Posted by sergeyrar123

Hi,

I want to find what will be left of number X, after 50 reductions of 2% - each time the reference is whats left from the total sum.

I was trying to find a general formula for this but without success.

x - 0.02X - 0.02(x-0.02x) - 0.02(x - 0.02X - 0.02(x-0.02x)) - ..... (N times)

please help me find a formula for N reductions.

1. If you reduce a value by 2% then there is left 98% of the original value.

2. With your example:

$N=1 : V = 50 - 50 \cdot \frac2{100} = 50 \cdot \frac{98}{100}$

$N=2 : V = 50 \cdot \frac{98}{100} - 50 \cdot \frac{98}{100} \cdot \frac2{100} = 50 \cdot \frac{98}{100}\cdot \frac{98}{100} = 50 \cdot \left(\frac{98}{100}\right)^2$

$N=3 : V = 50 \cdot \left(\frac{98}{100}\right)^2 - 50 \cdot \left(\frac{98}{100}\right)^2 \cdot \frac2{100} = 50 \cdot \left(\frac{98}{100}\right)^2\cdot \frac{98}{100} = 50 \cdot \left(\frac{98}{100}\right)^3$

... and so on. I guess you see that the 50th reduction of 50 is calculated by:

$V = 50 \cdot (0.98)^{50} \approx 18.21$

**sergeyrar123** · February 2nd 2013, 05:48 AM

YES !!
Thanks alot!

Thread: find a general formula for N reductions

LinkBack

Thread Tools

Display

find a general formula for N reductions

Re: find a general formula for N reductions

Re: find a general formula for N reductions

Similar Math Help Forum Discussions

General formula of a series

how would I find a general formula for f^(-1)''(x) ?

Find a general formula ...

General Formula

general integration formula

Search Tags