1. ## Difficult exponential equation

Hi,

I have two equations... I want to find the minimum number of years when S2>S1

S1= 0.5n(22000+(n-1)400)
S2= (10000(1.07^n -1)/(1.07-1))

I tried really really hard to solve this, but I ended up with some crap where n should be a negative number, which is impossible. The answer must be 6.33, btw)

I would very much appreciate it if anyone can help me out.

2. ## Re: Difficult exponential equation

Originally Posted by IBstudent
Hi,

I have two equations... I want to find the minimum number of years when S2>S1

S1= 0.5n(22000+(n-1)400)
S2= (10000(1.07^n -1)/(1.07-1))

I tried really really hard to solve this, but I ended up with some crap where n should be a negative number, which is impossible. The answer must be 6.33, btw)

I would very much appreciate it if anyone can help me out.

You will need to solve this either graphically of numerically.

CB

3. ## Re: Difficult exponential equation

Originally Posted by CaptainBlack
You will need to solve this either graphically of numerically.

CB
Can you please show me how to solve it numerically?

4. ## Re: Difficult exponential equation

Originally Posted by IBstudent
Can you please show me how to solve it numerically?
You want to find a positive root of the equation:

$S_1(n)-S_2(n)=0$

or:

$f(n)=0.5n[22000+(n-1)400]-\frac{10000(1.07^n -1)}{1.07-1}=0$

This is continuous and $f(1)>0$ and $f(7)<0$ so there is at least one root in the interval $(1,7)$.

Now see here for the general method:

CB

5. ## Re: Difficult exponential equation

Originally Posted by IBstudent
Hi,

I have two equations... I want to find the minimum number of years when S2>S1

S1= 0.5n(22000+(n-1)400)
S2= (10000(1.07^n -1)/(1.07-

I tried really really hard to solve this, but I ended up with some crap where n should be a negative number, which is impossible. The answer must be 6.33, btw)

I would very much appreciate it if anyone can help me out.