Answer
No, the model is not useful to predict the spread of a rumor after 1 month.
Work Step by Step
$N\left( t \right)=20{{\left( 3 \right)}^{t}}$ …… (1)
Now, put the value of $t$ in equation-1 as,
$\begin{align}
& N\left( t \right)=20{{\left( 3 \right)}^{t}} \\
& N\left( 30 \right)=20{{\left( 3 \right)}^{30}} \\
& N\left( 30 \right)=4.1\times {{10}^{15}}
\end{align}$
Thus, the number of people who heard the rumor after 1 month is $1.4\times {{10}^{15}}$; this number is very large and also exceeds the population of the U.S., so this number is not realistic.
Therefore, the model is not useful to predict the spread of the rumor after one month.
