a-rumor-spreads-in-a-school-according-to-dsdtas1sb-fracdsdt-as-left1-fracsbright

Question

A rumor spreads in a school according to dSdt=aS(1−SB) \frac{dS}{dt} = aS \left(1 - \frac{S}{B}\right) , where a a  is the spread rate, B B  is the total number of students, and S0 $$S_0  is $$the initial number of students who know the rumor. Find S(t) S(t)  in terms of aa, BB, S0S_0.

Accepted Answer

S(t)=BS0eat(B−S0)+S0eatS(t)=\frac{B $$S_0$$ $$e^{at}$$}{(B - $$S_0$$) + $$S_0$$ $$e^{at}$$}

Answer

S(t)=B(B−S0)+S0eatS(t)=\frac{B}{(B-$$S_0)+S$$_$$0e^{at}$$}

Answer

S(t)=BS0eat(B−S0)+eatS(t)=\frac{BS_$$0e^{at}$$}{(B-$$S_0$)+e^{at}$$}

Answer

S(t)=BS0eat(B+S0)−S0eatS(t)=\frac{BS_$$0e^{at}$$}{(B+$$S_0)-S$$_$$0e^{at}$$}

A rumor spreads in a school according to dSdt=aS(1−SB) \(\frac{dS}{dt}\) = aS \(\left\)(1 - \(\frac{S}{B}\]\right\)) , where a a is the spread rate, B B is the total number of students, and S0 S_0 is the initial number of students who know the rumor. Find S(t) S(t) in terms of aa, BB, S0S_0.

A rumor spreads in a school according to $\frac{d S}{d t} = a S (1 - \frac{S}{B})$ , where $a$ is the spread rate, $B$ is the total number of students, and $S sub 0$ is the initial number of students who know the rumor. Find $S (t)$ in terms of $a$ , $B$ , $S sub 0$ .