For the following situation f that determines the number of

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.

Solution

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)