A flu researcher is working under the assumption that the number of people who have the flu will double each day. If two people are infected with flu the first day, after how many more days will 64...

A flu researcher is working under the assumption that the number of people who have the flu will double each day. If two people are infected with flu the first day, after how many more days will 64 people be infected?

llltkl | Student

Since, the flu researcher is working  under the assumption that the number of people who have the flu will double each day,

Clearly, the no. of people infected each day  are in Geometric  Progression or G.P.  with no. of people infected on  the first day is 2 and total no. of people infected is 64.

So, the progression is:

2, 4, 8,.................................64

Let, the total no. of days people are infected be `n` , no. of people infected on the first day be `a`  and the common ratio of the no. of people getting infected each day be `r` .

Here, a=2, r= 2 , no. of people getting infected on the nth day= 64. Then,

`a_(n)=64`

`rArr a*r^(n-1)=64`

`rArr 2*2^(n-1)=64`

`=> 2^(n-1)=32`

`=> 2^(n-1)= 2^(5)`

`=> n-1=5`

`=> n=6`

Therefore, after (6-1) or 5 more days 64 people will be infected.

 

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