Xavier\'s little sister is doing a project for her second grade class to see how

Question

Xavier's little sister is doing a project for her second grade class to see how far around the world they can send a picture of their class hamster Jingles. He tells her that they can do this by sending an email to all the people he knows and then ask them to forward it on to three people that they know and so on. Jim has 128 people on his contact list and sends them the picture on day 1. On day 2, each recipient sends the email to 3 different people. On day 3, each of the new recipients sends the email to 3 different people. If the process continues, what is the total number of emails that will have been sent after day 7?

Explanation / Answer

Day 1 : Xavier sends email to 128 persons

Day 2 : 128 persons send email to 3 different persons each

Day 3 : Each of these 3 different persons send email to 3 new persons & so on the chain goes on.....

Now, when ONE person sends email to 3 different persons and each of those send email to 3 new persons & so on.... then the formula for such a sequence depicting number of people who will receive email on 'n' day is :

f (n) = 3n  (for n > 0)

so, in our question, after 'n' days, total number of emails is given by:

N = 128 + 128 * f(n-1)

[taking 'n-1' as chain starts from day 2]

N = 128 + 128*3n-1

N = 128*(1 + 3n-1) , the required algebraic equation

After 7 days, number of emails =

N = 128*(1 + 36)

= 128*(1 + 729)

= 128*730

= 93440 ANS

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