Answer
(a.) one student started the rumor in the class.
(b.) $18$ student in the class have heard the rumor after $6$ minutes.
Work Step by Step
The given formula is
$N=\frac{25}{1+24\cdot 2^{-t}}$
Where, Number of people in the class $ N $ who have heard the rumor after $ t $ minutes.
(a.)
The rumor started at $ t=0 $.
Plug above value into the formula.
$ N=\frac{25}{1+24\cdot 2^{-(0)}} $
$ N=\frac{25}{1+24\cdot 1} $
$ N=\frac{25}{1+24} $
$ N=\frac{25}{25} $
$ N=1 $.
(b.)
Given value of $ t $ is $ 6 $.
Plug above value into the formula.
$ N=\frac{25}{1+24\cdot 2^{-(6)}} $
$ N=\frac{25}{1+24\cdot \frac{1}{2^6}} $
$ N=\frac{25}{1+\frac{24}{64}} $
$ N=\frac{25}{1+\frac{3}{8}} $
$ N=\frac{25}{\frac{8+3}{8}} $
$ N=\frac{25}{\frac{11}{8}} $
$ N=25 \times \frac{8}{11} $
$ N=18.1818 $
$ N=18 $
