The number of cells in a tumor doubles every 3.0 months. If the tumor begains as a single cell, how many cells will there be after 3 years?
2007-11-04 02:19:42 · 6 answers · asked by cassie05 3 in Science & Mathematics ➔ Mathematics
0 month ..1 cell..2^0
3 months..2 cells...2^1
6 months..4 cells..2^2
9 months...8 cells..2^3
15months....32 cells...2^5
36months.....4096cells...2^12
2007-11-04 02:25:30 · answer #1 · answered by someone else 7 · 0⤊ 0⤋
3 years x 12 months = 36 months / 3 months = 12 doublings
1 x 2^12 = 1 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 4096
There will be 4096 cells after 3 years.
2007-11-04 10:26:16 · answer #2 · answered by Darrol 3 · 0⤊ 0⤋
there are 36 months in 3 years.
If it doubles every 3 months then it will double 12 times.
so 1 cell will become:
1 x 2^12 = 4096 cells
2007-11-04 10:27:06 · answer #3 · answered by k_l_k_l 3 · 0⤊ 0⤋
C = (1-2^(4*3)/(1-2)
C = 4095
This is a geometric series with r=2 and its sum is
[(a-r)^n]/(1-r), where a is the first term (in this case 1) and n is the number of terms.
The result is 4095, not 4096.
Since the first term is 1 and all the following terms ar even, the result must be odd.
2007-11-04 10:31:37 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋
since there is 12 months in a year you multiply 12 by 3 which is 36. then divide by3 because it is every 3 months which is 12.then start with one and double 12 times. you should get 4096 cells.
2007-11-04 10:27:18 · answer #5 · answered by mustangs_r4me 2 · 0⤊ 0⤋
0 -> 1 cell
3 months -> 2 cells
6 months -> 4 cells
9 months -> 8 cells
1 year -> 16 cells
15 months -> 32 cells
18 months -> 64 cells
21 months -> 128 cells
2 years -> 256 cells
27 months -> 512 cells
30 months -> 1024 cells
33 months -> 2048 cells
3 years -> 4096 cells
2007-11-04 10:27:08 · answer #6 · answered by PeterT 5 · 0⤊ 0⤋