Virus A deadly virus is killing people. Scientists from the entire world are studying the spread of this virus in the human body. Now they know that if a single virus enters the body of a patient, then after one hour s/he has 1000 virus. Furthermore, they know that there are actually three different subspecies of the virus: Subspecies A: The growth rate of virus A in the human body is proportional to the time elapsed since the first virus entered the body. If a single virus A enters the body of a patient, then after one hour s/he has 1000 virus A Subspecies B: The growth rate of virus B in the human body is proportional to the amount of virus B already present in the body. If a single virus B enters the body of a patient, then after one hour s/he has 1000 virus B Subspecies C: The growth rate of virus C in the human body is proportional to the difference between an upper limit of 1,000,000 and the amount of virus C already present in the body. If a single virus C enters the body of a patient, then after one hour s/he has 1000 virus C A virus of subspecies A will produce only more virus A, a virus of subspecies B will produce only more virus B and a virus of subspecies C will produce only more virus C The patient will die if s/he does not receive medicine before than the moment when there are 500,000 virus in her/his body. The scientists want to know which the most dangerous subspecies of virus is: A, B or C
Virus subspecies A shows a linear growth pattern since the
growth rate is based on time elapsed since first virus entry as
such it will continue to grow at 1000/hour
Virus subspecies B shows exponentially increasing growth pattern as
it is based on current population. This growth rate will double the
original value with every passing hour.
Virus subspecies C shows decreasing growth pattern as every
increase in population is measured against a growth rate
proportional to 1,000,000 minus the population. Hence with time
this speed of 1000/hr is likely to decrease to negligible
values.
Hence, Virus subspecies B shows the greatest danger
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