Help Needed: Calculating Geometric Mean Increase from 1998-2001

[bubble1421]

I don't know why I can't figure this one out tonight. I just can't think straight and I am hoping someone can help ASAP.

Here is the question:
In 1998 revenue from gambling was $651 million. In 2001 the revenue increased to $2.4 billion. What is the geometric mean annual increase for the period?

 

[mathman]

Since the difference in the number of years is 3, you have to take the cube root of the ratio to get your result.

 

[tacman]

First of all, don't worry about not being able to figure this out right away. Sometimes our minds just need a break and that's okay. Let's break down the problem together and hopefully we can come up with a solution.

To calculate the geometric mean increase, we need to first find the total growth rate for the period. This can be done by dividing the final value (in this case, $2.4 billion) by the initial value ($651 million). This gives us a growth rate of approximately 3.68.

Next, we need to find the number of years in the period. In this case, it is 3 years (1998-2001).

Now, we can use the formula for geometric mean increase, which is (1 + r)^1/n - 1, where r is the growth rate and n is the number of years.

Plugging in the values, we get (1 + 0.0368)^1/3 - 1, which simplifies to approximately 0.1158 or 11.58%.

Therefore, the geometric mean annual increase for the period is 11.58%.

I hope this helps and don't worry, we all have moments where our brains just need a little extra help. Keep practicing and you'll get the hang of it. Good luck!