viral marketing word problem

[Guest]

Here is my question I am to rusty to figure out:
If you were going to send 1,500,000 emails and 80% of them got opened, and of this 80% opened, 3% of them forwarded the email along to X number of people, what is the smallest possible number X can be so that this cycle can indefinitely perpetuate itself?

any help would be greatly appreciated.

 

[soroban]

Hello, bbb123!

If you were going to send 1,500,000 emails and 80% of them got opened,
and of this 80% opened, 3% of them forwarded the email along to X number of people,
what is the smallest possible number X can be so that this cycle can indefinitely perpetuate itself?

Since 80% x 3% = 2.4%, the number of forward letters is severely reduced at each forwarding.
\(\displaystyle \;\;\)Of your 1,500,000 emails, only 36,000 will forward it.

These 36,000 participants must (together) forward 1,5000,000 emails to perpetuate the cycle.

They must each forward \(\displaystyle 41\frac{2}{3}\,\approx\,42\) emails.

 

[stapel]

They must each forward \(\displaystyle 41\frac{2}{3}\,\approx\,42\) emails.

Just hope you're not on anybody's "forward" list! :evil:

Eliz.

 

[Guest]

ahhh

thank you both. dont worry, i will make sure you never get forwarded to! :wink: