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 \[{{2}^{3}}^{\times \text{ t}}.~\]
You need to login to perform this action.
You will be redirected in
3 sec