Question

How many cell divisions would it take to produce at least 1,000 cells from one cell? (When one cell splits in half during cell division, the result is two new cells. Each of those cells can divide into two more and so on.)

Answer (256?)

Answer 1

2^10 =1024 cells. So that means that the including the first division (1 into 2), there are 10 further divisions to reach 1024 cells. You can't get 1000 perfectly in this case. So total divisions is 11.

Answer 2

After 10 cell divisions 1000 cells will be produced from 1 cell.

Explanation:

This the case of exponential growth. The function that defines exponential growth is,

`y(t)=a(1+r)^t`

where

y(t) = the amount after time t,

a = initial amount,

r = rate of growth,

t = time period.

As the final amount is given to be 1000 cells from the initial amount of 1 cell, at the rate of 100% (because each cell will divide it self into new cell)

So here,

y(t) = 1000,

a = 1,

r = 100% = 1

Putting the values,

`\Rightarrow 1000=1(1+1)^t`

`\Rightarrow 1000=(2)^t`

`\Rightarrow \log 1000=\log 2^t`

`\Rightarrow \log 1000=t\log 2`

`\Rightarrow t=(\log 1000)/(\log 2)`

`\Rightarrow t=9.9\approx 10`

Therefore, after 10 cell divisions 1000 cells will be produced from 1 cell.