doubling Time #2-3

Question

Suppose that the number of cells in a tumor doubles every 5 months. Considering that the tumor begins with a single cell, answer the following:

 

How many cells will there be after 5 years?

Answer 1

f(x) = ab^x, where a = initial amount, be = rate of change, x = time.

 

2a = ab⁵     This is for the doubling in 5 months

2 = b⁵

2^1/5 = b

 

Now the the five years, 60 months.

 

f(60) = 1(2^1/5)⁶⁰

f(60) = 2¹²

f(60) = 4096

 

After five years 4,096 cells are present.

Answer 2

You can use the exponential growth function a(1 + r)^t, where a is the initial population, r is the growth rate, and t is the number of time intervals.

 

Five years is 60 months. The number of doublings in 60 months is 12 so t = 12. The percent growth is 100% so r = 1.

 

Plugging everything in gives 1(1 + 1)^12 = 4096 cells.