# Thread: Difference Equations

1. ## Difference Equations

Here's my question:

The answer to this probelm is:

$
S_{n} = 0.076 S_{n-1}
$

I don't see how to get this answer, here's my attempt:

Equation has to be of the form $S_{n} = k S_{n-1}$, where k is some constant. I don't understand how they've got k=0.076

Any explanation would be helpful.

2. Clearly this should be:

$S_n = 0.976 \, S_{n-1}$

so either you've mistyped it or the person who set the question mistyped it putting a zero in place of where the 9 should have been!

3. Originally Posted by the_doc
Clearly this should be:

$S_n = 0.976 \, S_{n-1}$

so either you've mistyped it or the person who set the question mistyped it putting a zero in place of where the 9 should have been!

Oh, ok, but how did you get 0.976?

4. Originally Posted by Roam
Oh, ok, but how did you get 0.976?
$S_{n} - S_{n-1} = -0.024S_{n-1}$

5. I'm sorry but I can't follow what you've done, could you please explain a little more?

6. Say after $(n-1)$ years the amount is $S_{n-1}$ so then after one more year you lose 2.4 % which is $0.024$ of $S_{n-1}$ so

the amount lost $= 0.024 S_{n-1}$ so then after $n$ years we have the amount $S_n$ given by the amount at the start of the year, $S_{n-1}$, minus the amount lost so

$S_n = S_{n-1} - 0.024 S_{n-1}$,

$= (1-0.024) S_{n-1}$,

$= 0.976 S_{n-1}$.

Any better?

7. ... How did you get 0.976?
100% - 2.4% = 97.6%