question_answer

The cells of a bacteria doubles in every 20 min. A scientist begins with a single cell.

(a) How many cells will be there after

(i) 10 h?

(ii) 25 h?

(b) What type of value is depicted by the cells of bacteria?

Answer:

(a) (i) The cells in bacteria double in every 20 min.

\[\because \] Number of cells in a bacteria after 20 min. = 2

\[\therefore \] Number of cells in bacteria after 40 min.

\[=2\times 2={{2}^{2}}\]

\[\therefore \] Number of cells in bacteria after 1 hr

\[=\text{ }{{2}^{2}}\times \text{ }2={{2}^{3}}\]

Number of cells in bacteria after 1 hr 20 min.

\[={{2}^{3}}\times 2={{2}^{4}}\]

Number of cells in bacteria after 1 hr 40 min.

\[={{2}^{4}}\times 2={{2}^{5}}\]

Number of cells in bacteria after 2 hrs

\[={{2}^{5}}\times 2={{2}^{6}}\]

\[={{\left( {{2}^{3}} \right)}^{2}}\]

\[\therefore \] Number of cells in bacteria after 10 hrs

\[={{\left( {{2}^{3}} \right)}^{10}}={{2}^{30}}~\]

(ii) Number of cells in bacteria after 25 hrs

\[={{\left( {{2}^{3}} \right)}^{25}}={{2}^{75~}}\]

(b) The value depicted by the cells of bacteria here is that it double itself after 20 min. in t hrs by \[{{2}^{3}}^{\times \text{ t}}.~\]