Today’s homework is inspired from an email I got from Simran,
I have a mathematical problem, I do not know if it can be solved using excel. So, the question is what is the probability of selecting a mutant cell if the percentage of mutant in the whole population is 0.01 and each cell is dividing 4 times per day,meaning at 2 raised to the power of 4 and the population is say 100,000 and is growing exponentially for 10 days and every day you are selecting, say 1/16 th of the population for the next growth? So, after 10 days, what are the chances that I have different mutants and not clone of the same mutant?
Let me break down the problem for you.
- We have a starting population of 100,000 cells (not the A1 kind)
- Out of which 1% are Mutant cells
- Each cell becomes 16 cells by end of day
- Naturally, there will be 1 new mutant cell for every 100 new cells produced in such a way.
- At the end of day, we just pick 1/16th of the cells and go for the next day
At the end of 10 days, what portion of total cells are,
- Normal (ie no mutation at all)?
- Clones of original Mutant cells?
- New Mutants?
What you need to do?
Simple. Make an Excel Model to simulate the cell mutation. Your objective is to find answers to above questions thru that model. (Obviously, we can find answers without modeling, but I want to see how we can creatively use Excel to solve a problem like this.)
Once you find a solution,
- Upload your workbook to skydrive or a public website
- You can also email to me at chandoo.d @ gmail.com with subject “mutant ninja turtle”
- Share the link thru comments along with a description of your solution
What if you don’t find mutant cells exciting?
Here is a mutant teddy bear. Enjoy it. (source)
More Excel Homework
If you enjoy excel challenges, then you will love Excel Homework page. It has a bunch of challenging exercises for you.
All the best. Go muse over the mutation problem.