Question

Scientists discovered a peculiar virus, which enters into a human body and gets doubled everyday. Find the number of viruses after $12$ days in a person's body who came in contact with this unknown virus.

• A. $2^{12}$
• B. $2^{11}$
• C. $2^{24}$
• D. $2^{22}$

Answer 1

The correct option is B $2^{11}$

On the first day, the number of viruses $=1=2^0$
On the second day, the number becomes $=2\times 2^0=2^{1+0}=2^1$
On the third day, the number of viruses $=2\times 2^1=2^{1+1}=2^2$
On the fourth day, it will be $=2\times 2^2=2^{1+2}=2^3$
.
.
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Similarly, on the 12th day, the number will be $=2\times 2^{10}=2^{1+10}=2^{11}$
So, on $12$th day, the person will have $2^{11}$ viruses in his/her body.