Doubling Times

Question

Suppose that the number of cells in a tumor doubles every 7 months. Considering that the tumor begins with a single cell, answer the following:

 How many cells will there be after 3 years?

(Check time units and round to the nearest whole number.)

How many cells will there be after 5 years?

(Check time units and round to the nearest whole number.)

Answer 1

3 years = 35

• 2^5 x 1.1 = 35

5 years = 380

• 2^8.5714 = 380

 

Answer 2

cells double every 7 month.

growth rate using rule of 70 = 10% per month.

3 yrs = 36 month = 7*5 + 1 month

ie in 3 yrs cells will double 5 times and then increase  10%.

 

so number of cells = 2^5 * 1.1 = 32 *1.1 = 35 (approximated to unit)

 

5yrs =60 m = 7*8 +4m

number of cells = 2^8 *1.1*1.1*1.1*1.1 =256* 1.4641  = 374 ( truncated to unit)