Total number of cancer cells inside a tumor: 100Each cell has a 10%

[goldfronts1]

Total number of cancer cells inside a tumor: 100
Each cell has a 10% chance of dying each time it divides
The rate at which a cell leaves the mass is 1 every 8 hours
The rate of division is 1 division / 2 hours

whats the time needed to attain the 100 cells in the first place?
What is the function that I could put in excel or MATLAB to figure this out quickly?

Not very good with coming up with the function.

I have the following:

0hrs x0 = 100
2hrs x1 = x0*0.90+x0
4hrs x2 = x1*0.90+x1
6hrs x3 = x2*0.90+x2
8hrs x4 = x3*0.90-1+x3

Thanks

 

[Valkarie]

.The time needed to attain the 100 cells in the first place can be calculated using a recursive formula. The formula is xn = xn-1*0.9 + xn-1, where xn is the number of cells at time n and xn-1 is the number of cells at time n-1. The function that could be used to calculate the time needed to attain the 100 cells in the first place is:x(n) = x(n-1)*0.9 + x(n-1)This function can be implemented in Excel or MATLAB by creating a loop that evaluates the expression above for each time step until the number of cells reaches 100.