Integration by Partial Fractions

[Kimmy2]

I honestly don't mean to put a question up to get answers. I truly am confused, and I want to understand this 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: b(lnp-(p-1))-ln(lna-(a-1))

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

(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 =

>> And for the last three sections, how do I incorporate them to my integral?

 

[galactus]

I honestly don't mean to put a question up to get answers. I truly am confused, and I want to understand this 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

\(\displaystyle bln\left(\frac{p(a-1)}{a(p-1)}\right)\)

(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: b(lnp-(p-1))-ln(lna-(a-1))

Remember the log laws: \(\displaystyle ln(a)-ln(b)=ln(a/b) \;\ and \;\ ln(a)+ln(b)=ln(ab)\)

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

Set your integral to 0 and sub in p=.08. Then, solve for a.

\(\displaystyle bln\left(\frac{.08(a-1)}{a(.08-1)}\right)=0\)

a=.08

Use the same method for the other three problems.