Question

VIRUS MUTATION
A new deadly virus has been accidentally injected into a patient at 8:30 AM. The species mutaties in such a way
that every individual produces exactly 2 offspring exactly after 1 hr. All individuals die exactly when offspring of
their 3rd generation produces their offspring. When the active population of the virus reaches 3900 the patient
will die. There is an antidote which will kill all virus if injected into the patient the very second it is
administered.
Find what is the max time before which the patient needs to be injected to be alive?
Note: Enter the time in 24 hour format. Eg. 1:45 PM should be entered as 13:45
3 Ashes
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Answer 1

Answer:

out of mind question pata nhiiii

Answer 2

Given the life cycle of a virus, find the max time to inject the vaccine before the patient dies.

Explanation:

• given that the virus multiplies after exactly one hour we can construct its population as                                                                                                [tex]0\ hr-> 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1^{st}\ generation\\ 1\ hr->2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2^{nd}\ generation\\ 2\ hr->1+2+2^2\ \ \ \ \ \ \ 3^{rd}\ generation[/tex]  
• now after the third generation produces their offspring that is when the fourth generation is formed all the individual die.
• Hence, we get the population after three hours as,                                              $3\ hrs->2^3 \ \ \ \ \ \ 4^{th}\ generation$      
• Hence after every hours that are multiple of three we get the population as,                                                                                                         [tex]6\ hrs->2^6=64\\ 9\ hrs->2^9=512\\ 12\ hrs->2^{12}=4096[/tex]    
• Since the maximum population of virus before the patient dies is $3900$ we can say that the max time is before $12\ hrs$ and more than $9\ hrs$.
• we get the populations between these hours as,                                            [tex]10\ hrs->2^9+2^{10}= 1536\\ 11\ hrs->2^9+2^{10}+2^{11}=3584\\ [/tex]  
• hence the time before the population reaches its maximum is between $11\ to\ 12\ hrs$
• since the virus produces offspring exactly after each hour we get the maximum time as ,                                                                                        [tex]max_{time}=8:30+12\\ max_{time}=20:30\ PM[/tex]     ------ANSWER