Answer
(a.) one student started the rumor in the class.
(b.) $10$ student in the class have heard the rumor after $4$ 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 $ 4 $.
Plug above value into the formula.
$ N=\frac{25}{1+24\cdot 2^{-(4)}} $
$ N=\frac{25}{1+24\cdot \frac{1}{2^4}} $
$ N=\frac{25}{1+\frac{24}{16}} $
$ N=\frac{25}{1+\frac{3}{2}} $
$ N=\frac{25}{\frac{2+3}{2}} $
$ N=\frac{25}{\frac{5}{2}} $
$ N=5 \times 2 $
$ N=10 $
