hacked into 2 accounts. Near the beginning of each of the following days, each hacked account sends links to 4 new accounts, which subsequently become hacked as well. By the end of the second day, IT support has found a way to restore users’ accounts, and 1 account has been restored at that point. Each day thereafter, 5 times as many accounts have been restored as the previous day. (a) Write a recurrence relation for the total number o
A phishing attack on a certain social media platform locks users out of their accounts
and spreads by sending malicious links to their followers to gain access to more accounts. On the
first day, the attack has hacked into 2 accounts. Near the beginning of each of the following days,
each hacked account sends links to 4 new accounts, which subsequently become hacked as well.
By the end of the second day, IT support has found a way to restore users’ accounts, and 1 account
has been restored at that point. Each day thereafter, 5 times as many accounts have been restored
as the previous day.
(a) Write a recurrence relation for the total number of hacked accounts at the end of day n.
(b) Solve the recurrence relation.
(c) How many days will it be until all users’ accounts have been completely restored?
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