Question 14 Marks
In a certain laboratory, scientists grow bacteria for research purposes. During a certain experiment, they rear bacteria in culture in a Petri dish. A particular strain of bacteria doubles in every 30 minutes. The scientists start with a single cell.
(1) How many bacteria will be there in the Petri dish after 12 hours?
(a) $2^{12}$$\quad$(b) $2^{18}$$\quad$(c) $2^{20}$$\quad$(d) $2^{24}$
(2) How many bacteria will be there in the Petri dish after 24 hours?
(a) $2^{24}$$\quad$(b) $2^{36}$$\quad$(c) $2^{40}$$\quad$(d) $2^{48}$
(3) If the Petri dish was full with bacteria after 24 hours, when was it half full?
(a) After 12 hours$\quad$(b) After 18 hours$\quad$(c) After 23 hours$\quad$(d) After 23 hours 30 minutes
(4) Had the scientists started with 1 cell each in two similar Petri dishes, how many bacteria would have been there in all after 12 hours?
(a) $2^{24}$$\quad$(b) $2^{25}$$\quad$(c) $2^{36}$$\quad$(d) $2^{48}$
(5) Had the scientists started with 2 cells in a Petri dish, how much time would they have saved in having a Petri dish full of bacteria?
(a) 30 minutes$\quad$(b) 1 hour$\quad$(c) 6 hours$\quad$(d) 12 hours
(1) How many bacteria will be there in the Petri dish after 12 hours?
(a) $2^{12}$$\quad$(b) $2^{18}$$\quad$(c) $2^{20}$$\quad$(d) $2^{24}$
(2) How many bacteria will be there in the Petri dish after 24 hours?
(a) $2^{24}$$\quad$(b) $2^{36}$$\quad$(c) $2^{40}$$\quad$(d) $2^{48}$
(3) If the Petri dish was full with bacteria after 24 hours, when was it half full?
(a) After 12 hours$\quad$(b) After 18 hours$\quad$(c) After 23 hours$\quad$(d) After 23 hours 30 minutes
(4) Had the scientists started with 1 cell each in two similar Petri dishes, how many bacteria would have been there in all after 12 hours?
(a) $2^{24}$$\quad$(b) $2^{25}$$\quad$(c) $2^{36}$$\quad$(d) $2^{48}$
(5) Had the scientists started with 2 cells in a Petri dish, how much time would they have saved in having a Petri dish full of bacteria?
(a) 30 minutes$\quad$(b) 1 hour$\quad$(c) 6 hours$\quad$(d) 12 hours
Answer
View full question & answer→(1) (D) $2^{24}$
Number of bacteria after 30 minutes $=2$.
Number of bacteria after two $30- min$ slots (i.e., 1 hour) $=2 \times 2=2^2$.
Number of bacteria after three $30- min$ slots (i.e., $1 \frac{1}{2}$ hours) $=2^2 \times 2=2^3$.
Number of bacteria after 24 slots of 30 min each (i.e., 12 hours) $=2^{24}$.
(2) (D) $2^{48}$
As shown above, number of bacteria after 48 slots of 30 min each (i.e., 24 hours) $=2^{48}$
(3) (D) After 23 hours 30 minutes
Since bacteria double after 30 minutes, so they were half in number 30 minutes before 24 hours, i.e., 23 hours 30 min .
(4) (B) $2^{25}$
$\begin{aligned} \text { Total number of bacteria in } 2 \text { Petri dishes after } 12 \text { hours } & =2^{24}+2^{24}=2 \times 2^{24} \\ & =2^{(1+34)}=2^{25} .\end{aligned}$
(5) (A) 30 minutes
On starting with 2 cells, there would be $2^{48}$ cells after 47 slots of 30 min each, i.e., after 23 hours 30 min . So, time saved $=30 min$.
Number of bacteria after 30 minutes $=2$.
Number of bacteria after two $30- min$ slots (i.e., 1 hour) $=2 \times 2=2^2$.
Number of bacteria after three $30- min$ slots (i.e., $1 \frac{1}{2}$ hours) $=2^2 \times 2=2^3$.
Number of bacteria after 24 slots of 30 min each (i.e., 12 hours) $=2^{24}$.
(2) (D) $2^{48}$
As shown above, number of bacteria after 48 slots of 30 min each (i.e., 24 hours) $=2^{48}$
(3) (D) After 23 hours 30 minutes
Since bacteria double after 30 minutes, so they were half in number 30 minutes before 24 hours, i.e., 23 hours 30 min .
(4) (B) $2^{25}$
$\begin{aligned} \text { Total number of bacteria in } 2 \text { Petri dishes after } 12 \text { hours } & =2^{24}+2^{24}=2 \times 2^{24} \\ & =2^{(1+34)}=2^{25} .\end{aligned}$
(5) (A) 30 minutes
On starting with 2 cells, there would be $2^{48}$ cells after 47 slots of 30 min each, i.e., after 23 hours 30 min . So, time saved $=30 min$.