- #1

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dx/dt = k*(50-[tex]\frac{2}{5}[/tex]*x)*(80-[tex]\frac{3}{5}[/tex]*x)

After separation and solving for partial fractions, I obtain:

[tex]\int\frac{1}{10-2*x}[/tex] - [tex]\frac{3}{2}[/tex][tex]\int\frac{1}{16-3*x}[/tex] = k*t+c

Which then yields:

[tex]\frac{16-3*x}{10-2*x}[/tex] = C*e[tex]^{2*k*t}[/tex]

C=8/5

k=[tex]\frac{ln(71/76)}{20}[/tex]

However, something is wrong with my final equation solved for x(t) due to x(0) doesn't = 0 and x(10) doesn't = 100.