I don't know why, but I am stuck on this seemingly easy question. Here's the question and the work I've done.(adsbygoogle = window.adsbygoogle || []).push({});

---------------------

A certain model for spread of rumors states that [tex]\frac{dy}{dt} = 3y(3-2y)[/tex] , where [tex]y[/tex] is the proportion of the population that has heard the rumor at time [tex]t[/tex]. What proportion of the population has heard the rumor when it is spreading the fastest?

--------

Ok. You are given the derivative of the proportion function, so setting it equal to 0 will give you when it is changing the fastest/slowest. Solving the equation [tex]3y(3-2y) = 0[/tex] you get 0 and 1.5....

Next part is to find the original equation and evaluate it at 1.5. So I will need to separate the variables, and when I do I get:

[tex]\frac{1}{3y(3-2y)}dy = dt[/tex]

This integral (I did it on my calculator) is [tex]\frac{-\ln{\frac{\mid2x-3\mid}{\mid{x}\mid}}}{9}[/tex]

When I evaulate 1.5 I get [tex]\infty[/tex]

Help me please.

Jameson

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Differential Equation Help

**Physics Forums | Science Articles, Homework Help, Discussion**