Worked example: Logistic model word problem | Differential equations | AP Calculus BC | Khan Academy

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Finding the carrying capacity of a population that grows logistically. Also finding the population's size when it's growing the fastest.
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[@ibraheemshaqqou7043]

I like to use the form dp/dt = kP(1-(P/A)) A being the carrying capacity.

[@sambad8429]

Thanks for the explanation. I have a question tho: how do we calculate the carrying capacity?

[@adesolao.2585]

based off what the video said about the logistics differential being a quadratic equation, i THINK, you could integrate the differential to get the quadratic and then solve for the vertex. which would just be (b, b/2a). but that would take more work than the logic given in the video

[@hritviktripathi8434]

Lim of the integral as it approaches infinity. Or in this differential equation in this video "a"

[@ekenennabuogor2591]

FIRST!!!!!! :D. thx for making this video, it really helped me out

[@mathewb5566]

Ekene Nnabuogor lol ture I don’t see any other comments and second!

[@brian77771]

Congrats what did you win?

[@ckyqq]

then why is the initial population of 700 given for, shouldn't it be (48000-700)/2?

[@Dinofx_jr]

Vatsal Bhargava No

[@kimikokimi]

I thought that too but I think the 700 is just in that scenario, in that problem. I think in general, you always do the half of the carrying capacity.

[@Rat_hunter_57]

@@Dinofx_jr ???

[@VASUDHARANIPATHEDAMIS]

I might be a bit late but yeah even I think the same ain't it (48000-700)/2

[@adesolao.2585]

@@VASUDHARANIPATHEDAMIS that’s assuming that the equation is linear. it’s not linear it’s a quadratic. i’m pretty sure in non linear equations, u can’t use the initial value to find to find the values of other parts of the equation edit: that’s unless u have the equation for the graph

[@lynncheung4189]

This is the hardest part for a highschooler so far

[@CountGrishnakh]

Im in calc AB but I still have these problems on my test tomorrow :(

[@aayaanfarooq9427]

What did you get

[@spacewombat]

It's "Petri dish", not "petry dish"!

[@TheHiddenChronicle-b9l]

No

[@Rat_hunter_57]

GRammar nazi

[@xdarkyoshi3161]

The image is too offensive

[@EliteCubingAlliance]

I'm doing this in algebra 2 😂😂

[@mrw5258]

Cap bruh imagine

[@Rat_hunter_57]

?

[@wakeupthisisntreal8168]

cap

[@EliteCubingAlliance]

No cap this is literally what I learned. My teacher had me do an exponential problem involving derivatives.

[@wakeupthisisntreal8168]

@@EliteCubingAlliance Then it's not algebra 2 cause you are actually taking a calculus course. No one learns derivatives in algebra so either you're lying or your school misnamed the class.