How Many Times Do I Have To Increase by 3%?

[piAreRound1]

I want to know how many time I have to increase 30 by 3% before it is greater or equal to 500.

I think this is the correct formula:
30 * 1.03^x >= 500

What steps do I have to take to solve it?

 

[MarkFL]

I would write:

\(\displaystyle 30\cdot1.03^n\ge500\)

Divide through by 30:

\(\displaystyle 1.03^n\ge\frac{50}{3}\)

Take the natural log of both sides, and apply a log rule to obtain:

\(\displaystyle n\ln(1.03)\ge\ln\left(\frac{50}{3}\right)\)

Hence:

\(\displaystyle n\ge\frac{\ln\left(\dfrac{50}{3}\right)}{\ln(1.03)}\)

Since presumably \(n\) is an integer, we could write:

\(\displaystyle n=\left\lceil\frac{\ln\left(\dfrac{50}{3}\right)}{\ln(1.03)}\right\rceil\)

This is the "ceiling" function and it tells us to round up to the nearest integer. According to W|A, we find:

\(\displaystyle n=96\)

Wolfram|Alpha: Computational Intelligence

 

[Wilmer]

I want to know how many time I have to increase 30 by 3% before it is greater or equal to 500.

Tattoo this on your wrist (under your watch!):

if a^p = b then p = ln(b) / ln(a)

 

[HOI]

My wrist is getting awfully crowded!