Answer
(a) $f(n)=6^{n}$
(b) After $4$ days.
Work Step by Step
(a) Since this process progresses like a geometric sequence, we can use the $n$th term formula for geometric sequence as the function that represents the number of people who have received the email after $n$ days.
First term $a_{1}=6$
Common ratio $r=6$
$f(n)=a_{1}r^{n-1}$
$\implies f(n)=6(6)^{n-1}=6^{n}$
(b) Given that $f(n)=1296$, we need to find $n$.
$6^{n}=1296$
Rewriting $1296$ as $6^{4}$, we get
$6^{n}=6^{4}$
Equating the exponents, we have
$n=4$.
