Thread: Integral Word Problem

A rumor is spread in a school. For 0<a<1 and b>0, the time t at which a fraction p of the school population has heard the rumor is given by


(a) Evaluate the integral to find an explicit formula for t(p). Write your answer so it has only one ln term.

>> So, I got: bln((p(1-a))/(a(1-p)))

(b) At time t=0, eight percent of the school population (p=0.08) has heard the rumor. What is a?
a = 0.08

(c) At time t=1, fifty percent of the school population (p=0.5) has heard the rumor. What is b?
b =

(d) At what time has ninety-five percent of the population (p = 0.95) heard the rumor?
t =

>>How exactly do I solve for the last 2 parts? How do I plug in the values?

Originally Posted by C.C.

A rumor is spread in a school. For 0<a<1 and b>0, the time t at which a fraction p of the school population has heard the rumor is given by


(a) Evaluate the integral to find an explicit formula for t(p). Write your answer so it has only one ln term.

>> So, I got: bln((p(1-a))/(a(1-p)))

(b) At time t=0, eight percent of the school population (p=0.08) has heard the rumor. What is a?
a = 0.08

So you now know that t(p)= b ln(p(1-.08)/(.08(1-p))

(c) At time t=1, fifty percent of the school population (p=0.5) has heard the rumor. What is b?
b =

Set p= 0.5, t(p)= 1 : 1= b ln(.5(1- 0.8)/0.8(1-.5)) and solve for b.

(d) At what time has ninety-five percent of the population (p = 0.95) heard the rumor?
t =

Once you know b, find t(.95)= bln(.95(1-0.8)/(0.8(1- .95)).

>>How exactly do I solve for the last 2 parts? How do I plug in the values?