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({});

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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?

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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

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# Differential Equation Help

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