For the following situation f, that determines the number of people who learned
ID: 3426407 • Letter: F
Question
For the following situation f, that determines the number of people who learned the secret on a given day. Let in represent the day number and f(n) represent the number and f(n) represent the number of people who learned the secret on day n. Assume that 6 people initially know the secret and on day 1 they each tell 2 people. Everyone who learns the secret on a given day tells the secret to 2 new people the next day. Assume that 3 people initially knew the secret and on day 1 they each tell 4 people. Everyone who learns the secret on a given day tells the secret to 4 new people the next day Assume that only one person initially knew the secret and on day 1 that person told 3 people. Everyone who learns the secret on a given day tells the secret to 3 new people the next day.Explanation / Answer
Solution: given f(n) is no. of people who learned the scret on given day and n is no. of day
a): initialy 6 people who know the secret and each tell two people on next day
on 1 day, people know the secret =6
on 2 day, people know the secret =6*2
on 3 day, people know the secret =6*2*2
and as like on n day, people know the secret =6*2*2*2....................n-1 times =6*2^(n-1)
and this is genral formula f(n)=6*2^(n-1)
b): 3 people know the secret on 1 day and each tell 4 people on next day
as like upper case analysis drive the expression f(n)=3*4^(n-1)
c): 1 people know the secret on 1 day and each tell 3 people on next day
as like upper most case analysis drive the expression f(n)=1*3^(n-1)= 3^(n-1)
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