For the following situations, define a function, f, that determines the number o

Question

For the following situations, define a function, f, that determines the number of people who learned the secret on a given day. Let n represent the day number and f(n) represent the number of people who learned the secret on day n. Assume that 6 people initially knew 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

a. Initinally 6 people knew and on day ,1 2*6=12 people knew and on the next day 12*2=24 people knew

Therefore the pattern is 12,24,48,96 .....

Required function is f(n)=6*2n

b. Initially 3 people knew and on day 1, 3*4=12 people knew and on the next day 12*4=48

Pattern is

12,48,192,...

required function is f(n)= 3*4n

c. Initially only one people knew and on day 1, 1*3=3 people knew and on next day 3*3=9 people knew

Pattern is 3,9,27,...

Required function is f(n)=1*3n

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