Question

How many hours after the culture was started and the maximum population is approximately what?

Answer 1

Check the picture below, so that's the picture of a parabolic path with a certain initial velocity.

so anyhow, not to bore you to death, the maximum or peak point occurs at the vertex, as you see in the picture, and the x-coordinate is how long it took to get there.

`\textit{vertex of a vertical parabola, using coefficients} \\\\ P(t)=\stackrel{\stackrel{a}{\downarrow }}{-1698}t^2\stackrel{\stackrel{b}{\downarrow }}{+85000}t\stackrel{\stackrel{c}{\downarrow }}{+10000} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 85000}{2(-1698)}~~~~ ,~~~~ 10000-\cfrac{ (85000)^2}{4(-1698)}\right) \implies \left( - \cfrac{ 85000 }{ -3396 }~~,~~10000 - \cfrac{ 7225000000 }{ -6792 } \right)`

`\left( \cfrac{ -21250 }{ -849 } ~~~~ ,~~~~ 10000 +\cfrac{ 903125000 }{ 849 } \right) \\\\\\ \left( \cfrac{ 21250 }{ 849 } ~~~~ ,~~~~ \cfrac{ 911615000 }{ 849 } \right) ~~ \approx ~~ (\stackrel{ hrs }{25}~~,~~\stackrel{ population }{1,074,000})`