Question

Question 124(ii)

The cell of a bacteria doubles in every 30 min. A scientist begins with a single cell. How many cells will be thereafter 24h?

Answer 1

The cell of a bacteria doubles in every 30 minutes.
If we begin with a single cell, then the cell of bacteria after

30 min =$2=2^1$
1 hour =$4=2^2$
1 hour and 30 min =$8=2^3$
2 hours =$16=2^4$
2 hours and 30 min =$32=2^5$
3 hours =$64=2^6$
4 hours =$2^8$
5 hours =$2^{10}$
$.....$
24 hours = $2^{48}$

Let x be the number of hours.
From the above we observe that the general term for the increase in the number of cell is $2^{2x}$
$\therefore NumberofCellsofabacteriain1hour=2^{2x}$
$=2^{2\times 1}$
$=2^2$

$\therefore NumberofCellsofabacteriain24hours=2^{2\times 24}$
$=2^{48}$