Exponential Growth

[@jenniferwang946]

Seven years later, these videos are still useful af.

[@Bozemanscience1]

I have heard that comparison (along with John Green and Alton Brown). I consider all of these compliments. I think they do great work. I met Hank when we were at KZbin headquarters and he is wonderful and he is from Montana. Double thumbs up.

[@gardenfairy947]

So glad I found this!! It was difficult to find any videos explaining population growth specifically, so thank you!

[@Gingerforlifeeee]

Thanks for posting these! I have learned more watching your videos than I have reading my biology book. I take my classes online and let me just say, these have been a true blessing.

[@hopepeterson7781]

Thanks SO much Mr. Anderson I was looking for a video to explain exactly this is preparation for the AP test tomorrow

[@Bozemanscience1]

Good questions: 1) It is a photographic backdrop. 2) I use the room lights. I tried using studio lighting for awhile but I got awful glare on my glasses. 3) I don't sit very close to the screen and I try to look at the camera rather than the screen. The choice of a black background on my Keynotes also help. Hope that helps.

[@zachlantz516]

This really clarified some things I was stuck on for an exam. Great video and great explanation!

[@GoodyChild7]

This was perfect I wish you were my teacher

[@jeannetteaok9420]

Much appreciated, English being my second language. I now get the meaning the word and this is enough for my comprehension within a sentence. Thank you!

[@MissAngelFaace]

Thanks SO much Mr. Anderson! I was looking for a video to explain exactly this in preparation for the AP exam next month!

[@punkifob]

thank you!!! understood after hours of confusion!

[@mus1307]

What a good pedagogical teacher. Thanks for those smart tools you used to explain us !

[@thebignoob1569]

Your explanations are so clear!

[@Bozemanscience1]

That is frustrating. It works fine on this end. Please let me know if anyone else is having similar issues.

[@horizonbrave1533]

lol, I love the death animation is the rabbit burtsting into flame.... But how does this relate to the number 'e'?

[@haleywunderlich2313]

I have my AP biology final tomorrow and I watched about 10 of your videos. I would just like to tell you how incredibly helpful your videos are and how much I wish you were my teacher. Everything makes so much more sense! Thank you :) I think I will do better on my final due to your videos

[@hovhadovah]

It also helps a lot if you've taken AP Calculus and are familiar with differential equations. It makes things a lot easier in terms of understanding the notation.

[@shelleywell1]

THANK YOU MR ANDERSON YOU ARE OUR SCIENCE UNDERSTANDING SHRINE WITHOUT PAIN ,THANK YOU

[@Bozemanscience1]

Hunter. When you fill the spreadsheet down it will change B2 accordingly. For example the next box down will include B3+0.3B3. Since B3 has increased it will increase as well.

[@noobmaster-gc2nd]

Ok bozo 😂😂😂👌👌✅✅

[@1314Fher]

Yeeeeees! I need this. Thank you!

[@emmaandersson1730]

Thank you soooo soo much!! This has really helped me a lot!! :)

[@lauratomlinson1035]

Ohh Mr. Anderson looking good :D Also I like your videos! (P.s being english, I love your accent!)

[@Ducklingproductions0]

Biology revision done for the day, watching 10 or so videos! Thanks, these are really helpful!

[@human.earthling]

On excel, you can just double click at the bottom right of the cell with the formula and it will automatically "drag" it down as far as the numbers go, instead of having to manually drag it like you do at 5:48

[@martysalas2566]

Very helpful video. I understand the concept after watching this video:)

[@hahaLOLimlaughing]

This is so helpful! no wonder my own ap bio teacher made me watch it for homework... :) It definitely helped me understand

[@MartinaYow]

Thank you so much!!! I couldn't find anything to help with my kiddo's Ecology homework. Super user friendly.

[@fastertempo]

Thank you so much! I have recently struggled very much in a math class that I unfortunately had to drop out of :( I needed to learn quickly how to do Exponential Growth for my new math class and you taught me in 10 minutes! Thanks, Eric

[@flaviaoliveira5949]

You are a great teacher, thank you.

[@corradoblondi9792]

You're a great teacher!!

[@avani3510]

thank you so much i was so confused by this because i missed the day my teacher went over it but i understand it now

[@science-bite-size]

Great video - that part that I could watch. Somewhere around 3:30 the sound gets desynchronized from the video and then sometime later the image goes blurry then sound disappears completely.

[@Educationbanglaa]

THANK YOU very much . Love from India EASILY UNDERSTOOD

[@NeuroCurieux]

Super clear and entertaining as always! On my channel I use the example of $$$ increases also using Excel to introduce exponential growth

[@divermike8943]

At least 3 of us have the same question: Where did N0(t)=N0(1+R)^t come from. In your spreadsheet you are using N(t)=Sum(Nn+R*Nn)=Sum[Nn(1+R)] with n=0 to n=t Don't know how to type the Summation Notation here. I checked and iteratively summing Nn(1+R) from n=0 to n=t does give you the same values as N(t)=N(0)*[1=R]^t but I'd like to see the algebra that gets you there. That is how did you get the closed-form solution? Also the solution to the diff equation dN/dt=RN is N(t)=N*e^r(*t ) as Ceilia Jennings mentions below.

[@OnepieceSlayer]

Well done!

[@tshililomulaudzi6571]

Wow, thank you, now I am sure of my answers.

[@frankieroandMCR]

better than my university lecturers!

[@coolprofcp3814]

Thank you for all the great videos. I have a few general questions but I did not know where would be appropriate to post. So, here they are and I hope you will reply: (1) Is the background a photographic backdrop as it appears in videos or is it a green screen? (2) do you use additional video lighting beyond the room light? (3) how do you avoid computer monitor reflection on your glasses or the blue/green light of the monitor on the face? A picture of the setup would be wonderful. Thanks.

[@Mckreelove]

My Heroo! thank you so muchh i really wish i could officially meet you and have some bio lessons =D

[@uniramia4]

great video!

[@silencedidgood]

You do great work (my daughters will have just missed it) but somehow euler has been left out of the discussion. When you get a chance you should check out the discussion at better explained ...do a web search. Keep it up...perhaps my grand kids will use your stuff.

[@tigershell1]

Thanks for the help!

[@twowheelworld]

Great video, thank you!

[@Dyenosoreusrex]

Oh thanks for clearing it up.

[@nephophile3003]

THANK YOU SO MUCH!

[@meowmeowkittycatmeowmeow]

I find your videos incredibly helpful so thank you so much!!! Btw, has anyone told you how much you look like Hank Green (from the vlogbrothers)?

[@bevanlouis5646]

you get two different answers when using the two equations provided for exponential growth.............. N.e^(r.t) and N(1+r)^t....which one do we use ????????

[@coordenacaobiologiaufpr296]

I have the same question

[@youngchase3636]

BRILLIANT....thanks a lot!

[@emilywexler9238]

Works fine on my end. Great videos :)

[@shirlann9899]

THX, the video was very informative.

[@deepthireddyvasi2075]

was a wholesome vid indeed.

[@GDonPadlan]

Greetings Mr. Millard's H Biology class!

[@BubblesandCake]

You are my hero.

[@bouclesbrillantes127]

Thank you 😊

[@1farhinmomtazriana25]

Thanks a lot Sir. It was really helpful.

[@amasian16]

This is super helpful! T hank you!!

[@ernestturner2415]

Can you please make a video on how to solve exponential growth word problems. I just cant understand how to do exponential growth.

[@UntilWeGotCaught]

Thank you so much! God Bless

[@sealion_xo]

Why does using N(t)=N(1+r)^ t, give you different results than if you used N(t)=Nexp^r*t . My professor gave me the latter, and I tried to apply it to the same problems you were doing at the end, but it gave different results.

[@leticiamartinez9373]

Did you have an answer to your question? I am wondering the same thing?

[@divermike8943]

Yes Me too. Are these just different exponential models? I know that solve the diff eq. dN/dt=rN yields N(t)=Ne^(r*t). Where does N(t)=N(1+R)^t come from

[@AlwaysLoudAA]

Hello Mrs.Husinga class!

[@adiverma4712]

hello Mr Andersen, why didn't you use formula Nt=N.e^rt ?????

[@lovelyfrenzy1]

How would you find an estimate of just population (N)? Is there a formula for finding (N)?

[@DIANA4972]

thank you, I think I get this now :) FINALLY

[@nat_han]

Glad they're only virtual rabbits

[@MrPrabhubct]

Nice. Thanks.

[@lil_lady8403]

When you solve a population size over time what do you mean by the power for example you did (1.3)^30 but how did you get (2619.9)?

[@davidschwarz2530]

Video and sound work for me ~ David S

[@Dyenosoreusrex]

That doesn't make any sense. The formula was B2+0.3*B2. B2 is 10 so 10+0.3*10 should always be the same answer?

[@cluelessdevice787]

Watching this on my iPhone, right after you talk about the population increasing to 29 the audio stops working...

[@uhlicawu]

totally saw both john green and alton brown! the scientific version! :)

[@EllyKSaysHi]

is limits only related to calculus?

[@evanshui4653]

Linton sent me here.

[@rodgersotokoma8289]

Awesome..

[@kimberlykv4313]

How do you determine how many deaths there is?

[@simplebio7489]

Super

[@Galaxy95311]

I love u so much thank you

[@aumnamahshivaya6086]

Tq🙏

[@casss320]

Bless you. Please teach my ap bio class.

[@peaceking211]

"then I want to kill rabbits, don't worry they are just virtual rabbits" -- we see deep into this statement. Don't forget kuru disease and judgements soon to come upon all those who have killed "virtual" rabbits (definition of virtual: almost or nearly as described, but not completely) We see you. We understand you.

[@silentbitbeadly8652]

Tanks

[@markdonaj264]

Mr Folsom?

[@zoharwolfson8914]

This helped sooooooo much!! Yay Algebra one.. not really...

[@sj.shewolf8435]

Zo Wo I have accelerated algebra 😲😖

[@mervonium]

Reminds me of compound interest

[@elizabethcrawford9356]

if there are 3.9 rabbits, wouldn't you round down to 3 since you cannot have .9 of a rabbit?

[@Mornys]

+elizabeth crawford Sure you can have f.e. 3,9 rabbits when one rabbit is carrying and is 90% in term. Also how about Pistorius? =P

[@hannahshaler2101]

elizabeth crawford you would round to 4

[@iammichelewithonel]

They're just virtual rabbits hahahaha

[@gold_lychee]

omg thank you

[@stephenkrus]

Weird... I fully understand this. So... the grown rate is nothing but multiplier that increases really fast over time. Hmm... 🤔

[@milaguzc]

he is killing rabbits, this is not okay. I demand a court date for him to go to trial for death of rabbits

[@michaelseanchang]

Im not okay with killing bunnies, whether virtual or physical. change your ways.

[@shelleywell1]

+Michael Chang GROW UP , HE SAID ITS VIRTUAL , GET A GRIP

[@shelleywell1]

I WILL CALL THE POLICE FOR YOU .IF YOU DID NOT GROW UP.

[@buda1841]

realy????????

[@buda1841]

*Really??????????????????????????????????????????????????????

[@CrazyGamer-xi8rf]

Tell that to the Australians

[@xdustymanx]

why you burn the rabbitssssssssssss???????

[@fairyqueen4143]

Wow

[@xiiixiiih.16]

💡🍎✌️

[@troybrinson19]

Ok sir

[@carloemanueledoria7648]

tseries favorite video

[@agdoombagdoom8540]

There are just virtual rabbits 😊

[@chrismedbury2049]

i hate tis crap but I gotta larn it lmao

[@xtourmaline]

they’re just virtual rabbits..

[@kevinlam1828]

roooney

[@mervonium]

This formula re,i