Question 14 Marks
Ramlal is the incharge of a laboratory. In a bacteria culture under observation in his laboratory,the population of bacteria doubles every hour. When Ramlal started the observation, there were100 bacteria.
Q.1. Which of the following expressions gives the bacterial population after n hours?
(a)$\frac{100}{2^n}$$\quad$(b) $\frac{100}{2^{n-1}}$$\quad$(c)$2^n \times 100$$\quad$(d) $2^{n-1} \times 100$
Q.2. The population size of the bacteria after 3 hours will bе
(a) 800$\quad$ (b) 300$\quad$(c) 600$\quad$(d) 120О
Q.3. How many bacteria will be there in the culture after 1 day?
(a) $\frac{100}{2^{12}}$$\quad$(b) $2^{24} \times 100$$\quad$(c) $2^{12} \times 100$$\quad$(d) $\frac{100}{2^{24}}$
Q.4. Ramlal observes the culture after every one hour. Find the number of hours after which the population size of the bacteria will be larger than 3000.
(a) 5 hours$\quad$(b) 6 hours$\quad$(c) 7 hours$\quad$(d) 8 hours
Q.1. Which of the following expressions gives the bacterial population after n hours?
(a)$\frac{100}{2^n}$$\quad$(b) $\frac{100}{2^{n-1}}$$\quad$(c)$2^n \times 100$$\quad$(d) $2^{n-1} \times 100$
Q.2. The population size of the bacteria after 3 hours will bе
(a) 800$\quad$ (b) 300$\quad$(c) 600$\quad$(d) 120О
Q.3. How many bacteria will be there in the culture after 1 day?
(a) $\frac{100}{2^{12}}$$\quad$(b) $2^{24} \times 100$$\quad$(c) $2^{12} \times 100$$\quad$(d) $\frac{100}{2^{24}}$
Q.4. Ramlal observes the culture after every one hour. Find the number of hours after which the population size of the bacteria will be larger than 3000.
(a) 5 hours$\quad$(b) 6 hours$\quad$(c) 7 hours$\quad$(d) 8 hours
Answer
View full question & answer→1.(c): The population of bacteria doubles every hour.
Bacterial population after 1 hour $=2 \times 100$.
Bacterial population after 2 hours $=2 \times(2 \times 100)=2^2 \times 100$.
Bacterial population after 3 hours $=2 \times\left(2^2 \times 100\right)=2^3 \times 100$.
$\therefore$ the bacterial population after $n$ hours $=2^n \times 100$.
2. (a): Bacterial population after 3 hours $=2^3 \times 100=8 \times 100=800$.
3. (b): After 1 day, i.e., after 24 hours, the bacterial population will be $=2^{24} \times 100$.
4. (a): Bacterial population after 1 hour $=2 \times 100=200$;
after 2 hours $=2^2 \times 100=400$;
after 3 hours $=2^3 \times 100=800$;
after 5 hours $=2^5 \times 100=3200$.
So, the bacterial population will be larger than 3000 in 5 hours.
Bacterial population after 1 hour $=2 \times 100$.
Bacterial population after 2 hours $=2 \times(2 \times 100)=2^2 \times 100$.
Bacterial population after 3 hours $=2 \times\left(2^2 \times 100\right)=2^3 \times 100$.
$\therefore$ the bacterial population after $n$ hours $=2^n \times 100$.
2. (a): Bacterial population after 3 hours $=2^3 \times 100=8 \times 100=800$.
3. (b): After 1 day, i.e., after 24 hours, the bacterial population will be $=2^{24} \times 100$.
4. (a): Bacterial population after 1 hour $=2 \times 100=200$;
after 2 hours $=2^2 \times 100=400$;
after 3 hours $=2^3 \times 100=800$;
after 5 hours $=2^5 \times 100=3200$.
So, the bacterial population will be larger than 3000 in 5 hours.