Logistic Growth Function and Differential Equations

This calculus video tutorial explains the concept behind the logistic growth model function which describes the limits of population growth. This shows you how to derive the general solution or logistic growth formula starting from a differential equation which describes the population growth rate. This video contains 1 example problem with multiple parts.
Algebra For Beginners:
• Algebra For Beginners ...
Logarithms - The Easy Way!
• Logarithms - The Easy ...
Solving Exponential Equations:
• Solving Exponential Eq...
Solving Logarithmic Equations:
• Solving Logarithmic Eq...
Logarithmic Equations - Different Bases:
• Solving Logarithmic Eq...
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Compound Interest Word Problems:
• Compound Interest
Interest Compounded Continuously:
• Interest Compounded Co...
Population Growth Word Problems:
• Compound Interest & Po...
Logarithms Practice Problems:
• Logarithms - Practice ...
Where does "e" come from?
• Logarithms - e - Euler...
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Logistic Growth Function:
• Logistic Growth Functi...
Newton's Law of Cooling:
• Newton's Law of Coolin...
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/oWjQY61ml72Sqsk Final Exams and Video Playlists: www.video-tutor.net/

[@ronalddaugherty]

I wish more instructors had your teaching style. You pick the perfect times to pause to let your viewers absorb what you just explained. A lot of instructors don't give their students time to absorb the material before they are throwing another concept at you.

[@Kevin-zf5zz]

I’m gonna watch every god damn ad in your video man. You’re so helpful

[@sunnybiswas5249]

An easy way of calculating the b value is by the formula ( L - A)/ A where L is the carrying capacity ( as seen in the video) and A being the initial population. For example, in the first word problem with the dogs on the island, the carrying capacity was 5000 and the initial population was 100. Therefore the b value can be calculated by (5000-100)/ (100) = 49. Please note that I have only seen up until the first problem where this was not mentioned at the time, in case he mentioned it later. Hope this helps!

[@ellieshoulders3577]

YOU ARE AMAZING! Thank you so much

[@patrickalava1266]

Crystal clear explanation with a useful refresher on integration by partial fractions. Well done!

[@kevinmackie4045]

Super well done video. Needed to understand this better for a Calculus project. Thank you for sharing!

[@josephineeffah8767]

wow. I just love your tutorials , you are a real gem

[@earnesttechie1494]

Actually, I couldn't understand the concept of logistic regression for data science before. But, after watching your video, it gave me a clear-cut definition. Thank you very much.. Sir.. ❤️❤️❤️❤️

[@eddyarmelkayuzi5891]

That's an ultimate example of perfect tutoring

[@QuanTran-bb9zw]

Well explained video, I have a quiz tomorrow and feel more prepared now. Thank you so much for all you do!

[@nicklanham8014]

That's all you got?! mic drop ur the man ily

[@kamvc72]

Have a note while having his lecture, its so worthwile..

[@cinticotz2867]

Thanks for all lectures and merry christmas

[@hedy7548]

23:54 another way to get B which is much less prone to mistakes is B = ( carrying capacity - P(initial) ) / p(initial) ....... B = (5000 - 100) / 100 = 49

[@colemannina2371]

I love your videos

[@withloveandflowers]

This helped me so much! Thank you!! 🙏

[@emmanuel-luka]

Nice video explains the logistic growth model step by step

[@RavinduViduranga]

I could undestand it Thankz kepp it up !✌✌

[@yuanyuanli8822]

really helpful for understanding this chapter!!!!Thx^^

[@shaheerl]

one of the best EVER

[@kristinwomack1150]

I love your videos too.

[@user-yb9fb3mf1w]

I'm not entirely sure why this is in the Precalculus playlist when the entire video is basically just using Calculus?

[@beijingwazzup2374]

Ya gotta learn to run before learn to walk

[@gunnertyme7414]

​@@beijingwazzup2374 real

[@dwarvenminer3329]

Most universities will have a statistice course that uses the simplest forms of calculus before the deeper derivation and integration. Usually you'll have 1 or 2 formulas for the integration and derivatives given and you just apply them based on visual analysis before have them fully explained.

[@michaelgebremeskel6622]

Thanks brother I really appreciate

[@georgesadler7830]

MR. Organic Chemistry Tutor, this video/lecture is a basic introduction to Logistic Growth and Differential Equations that describes population growth. This equation is well known in mathematics and nature.

[@jealouseggs5619]

goddamn this gy has a video on freaking everything

[@sanopann1896]

do i need to calculate the general solution for logistic equation if i can memories it

[@franciscaoketa1399]

Thank you Prof

[@miker6385]

Pure genius!

[@sprezzaturarrd]

can you compute the basic reproduction number, R0, from the constants: k and b?

[@orwahassan821]

Beautiful.

[@giuliabaratta5350]

thank you so much

[@kiraivanova1342]

👏👏👏👏thank you man

[@ammarhasan2476]

beautifully explained

[@WeynBadillo]

Thank you!

[@solutionbybrain9978]

Super channel

[@TheGibberingGoblin]

cheers legend

[@franciscov761]

Hi! What happens if your carrying capacity (max capacity) is equal to the value of your initial condition? I have P(0)=2500 ; with a carrying capacity of 2500, so my B is 0?

[@pepethefrog6837]

There wouldn't be a logistics curve 😂 just a straight line

[@balajihariharan7175]

yes

[@1AWUK]

anyone know how he works out the ln value of (4/49) ? because he just says it and i don't know how he gets there, or if it is a setting on the calculator?

[@1AWUK]

dw found it lol

[@Reechard01]

Please how can I get time when y approaches limit

[@stevenp7553]

At 16:27 I wonder why we don't add c in the left side. I've be confused for a long period.

[@aitchbee]

Think of left side C as C sub 1 and right side C as C sub 2. C=Csub2-Csub1. Since both are constants they can be combined i

[@zubair1424]

All of your videos up this one have been amazing. Can you redo this one? Seems like it wasn't as clear

[@disarmthagun2272]

How do you do the derivative of L/(1+e^(-kt))

[@carultch]

With respect to which variable? If you had t in mind as the variable of differentiation, this is how you'd do it: Use the chain rule. Let u =1 + e^(-k*t). This gives us L/u. Find d/du of this, using the power rule: d/du L/u = -L/u^2 We don't want d/du, we want d/dt. So multiply by du/dx: du/dt = d/dt (1) + d/dt (e^(-k*t)) = 0 - k*e^(-k*t) Plug in for u: -L/(1 + k*e^(-k*t)) * (-k*e^(-k*t)) Simplify, and get: L*e^(-k*t)/(1 + k*e^(k*t))

[@danielfrt]

the derivative of this logistic curve is wrong, the correct one would be p(t)'=(5000*t*49*2.71828^(-.174*t))/(1+49*2.71828^(-.174*t))^2 and then it matches if you graph both functions.

[@ricky5870]

mistake was at 15:28 i think (LHS)

[@sanopann1896]

dammit i have no idea whats going on but still watching

[@raksharajak7091]

What is b denotes... Pls ans

[@GiangNguyen-ye2ll]

you can denote any constant using any letter, in this case is b

[@hugoeriksson6524]

Watch at 1.5x speed to get the Ben Shapiro experience

[@pezpeculiar9557]

sounds like hell

[@BrandonSLockey]

big brain

[@giuliapiccinini7343]

I think I am in love with you after this

[@Mindyourbusiness614]

I still don't understand how you are simplifying the "e" exponent. That step needs much more explanation.

[@Beanmachine2]

He never answered how many dogs were being born in 2016... only told us the net increase and different ways to find it.

[@OkGonzo]

21:31

[@dildobaggins2759]

quite a bit of the question is memorization and not necessary for me to know atm adios ime outta here...

[@aryaashari8954]

:))

[@wallgolfing]

Jesus Christ is Lord, King and Our Savor!

[@oro-oluwatoromo-thewordoft7339]

thank God!!!!! may God be with us all and keep us all in the mighty name of Jesus Amen! May we all live for over a hundred years with long life, good health and prosperity to glorify the mighty name of God! and may we live to go to heaven at the end in the mighty name of Jesus Amen! and remember we are not alone, God is with us and God loves us: remember this bible verse: For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future thank God!!!!!!!! Jerimiah 29:11

[@kristianchoate5869]

Could you possibly not shove your religion down people's throats in the comment section of a calculus video?? Thanks