Originally Posted by

**CaptainBlack** The question is asking you to find the largest $\displaystyle k$ such that:

$\displaystyle 100 \left( \frac{11}{17} \right)^{k-1}-50 \left( \frac{14}{17} \right)^{k-1}>14$

RonL

Originally Posted by

**Fishsticks** Thank you for your help, I however still can't figure out how to solve it.

It may be asking a bit much, but could you walk me through solving it so I can better understand what was required? Thanks.

You start with $\displaystyle k=1$ and check if:

$\displaystyle 100 \left( \frac{11}{17} \right)^{k-1}-50 \left( \frac{14}{17} \right)^{k-1}>14$

if so try $\displaystyle k=2$, ..

Being lazy I automate this as in the code fragment below, to find the required $\displaystyle k$ is $\displaystyle 2$.

Code:

>
>k=[1:5]
Column 1 to 3:
1 2 3
Column 4 to 5:
4 5
>
>100*(11/17)^(k-1)-50*(14/17)^(k-1)
Column 1 to 3:
50 23.5294 7.95848
Column 4 to 5:
-0.834521 -5.46809
>

RonL