Answer:
After 10 cell divisions 1000 cells will be produced from 1 cell.
Step-by-step explanation:
This the case of exponential growth. The function that defines exponential growth is,
[tex]y(t)=a(1+r)^t[/tex]
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,
[tex]\Rightarrow 1000=1(1+1)^t[/tex]
[tex]\Rightarrow 1000=(2)^t[/tex]
[tex]\Rightarrow \log 1000=\log 2^t[/tex]
[tex]\Rightarrow \log 1000=t\log 2[/tex]
[tex]\Rightarrow t=\dfrac{\log 1000}{\log 2}[/tex]
[tex]\Rightarrow t=9.9\approx 10[/tex]
Therefore, after 10 cell divisions 1000 cells will be produced from 1 cell.
