Exponential Growth

Paul Andersen explains how populations experience exponential. He begins by address the major players; N (population size) and r (growth rate). He models population growth in rabbits through four generations. He then shows you how to use a spreadsheet and then algebra to predict future populations.
Intro Music Atribution
Title: I4dsong_loop_main.wav
Artist: CosmicD
Link to sound: www.freesound.org/people/Cosmi...
Creative Commons Atribution License
All images are either Public Domain or Creative Commons Attribution Licenses:
Nevit. English: White Rabbit, 2011. Own work. commons.wikimedia.org/wiki/Fi....

Пікірлер: 116

  • @Bozemanscience1
    @Bozemanscience111 жыл бұрын

    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 KZread headquarters and he is wonderful and he is from Montana. Double thumbs up.

  • @jenniferwang946
    @jenniferwang9463 жыл бұрын

    Seven years later, these videos are still useful af.

  • @gardenfairy947
    @gardenfairy94710 жыл бұрын

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

  • @Bozemanscience1
    @Bozemanscience111 жыл бұрын

    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.

  • @hopepeterson7781
    @hopepeterson778110 жыл бұрын

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

  • @Gingyschroniclife
    @Gingyschroniclife4 жыл бұрын

    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.

  • @MissAngelFaace
    @MissAngelFaace10 жыл бұрын

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

  • @zachlantz516
    @zachlantz5169 жыл бұрын

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

  • @GoodyChild7
    @GoodyChild79 жыл бұрын

    This was perfect I wish you were my teacher

  • @thebignoob1569
    @thebignoob15693 жыл бұрын

    Your explanations are so clear!

  • @horizonbrave1533
    @horizonbrave15335 жыл бұрын

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

  • @Bozemanscience1
    @Bozemanscience111 жыл бұрын

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

  • @jeannetteaok9420
    @jeannetteaok94203 жыл бұрын

    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!

  • @mus1307
    @mus13078 жыл бұрын

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

  • @punkifob
    @punkifob10 жыл бұрын

    thank you!!! understood after hours of confusion!

  • @1314Fher
    @1314Fher9 жыл бұрын

    Yeeeeees! I need this. Thank you!

  • @emmaandersson1730
    @emmaandersson17308 жыл бұрын

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

  • @Ducklingproductions0
    @Ducklingproductions011 жыл бұрын

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

  • @hovhadovah
    @hovhadovah8 жыл бұрын

    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.

  • @flaviaoliveira5949
    @flaviaoliveira59494 жыл бұрын

    You are a great teacher, thank you.

  • @fastertempo
    @fastertempo10 жыл бұрын

    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

  • @corradoblondi9792
    @corradoblondi97923 жыл бұрын

    You're a great teacher!!

  • @Bozemanscience1
    @Bozemanscience111 жыл бұрын

    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

    @noobmaster-gc2nd

    3 жыл бұрын

    Ok bozo 😂😂😂👌👌✅✅

  • @lauratomlinson1035
    @lauratomlinson103511 жыл бұрын

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

  • @tigershell1
    @tigershell16 жыл бұрын

    Thanks for the help!

  • @martysalas2566
    @martysalas25662 жыл бұрын

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

  • @shelleywell1
    @shelleywell18 жыл бұрын

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

  • @OnepieceSlayer
    @OnepieceSlayer3 жыл бұрын

    Well done!

  • @twowheelworld
    @twowheelworld11 жыл бұрын

    Great video, thank you!

  • @nephophile3003
    @nephophile3003 Жыл бұрын

    THANK YOU SO MUCH!

  • @youngchase3636
    @youngchase363610 жыл бұрын

    BRILLIANT....thanks a lot!

  • @human.earthling
    @human.earthling8 жыл бұрын

    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

  • @meowmeowkittycatmeowmeow
    @meowmeowkittycatmeowmeow11 жыл бұрын

    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)?

  • @coolprofcp3814
    @coolprofcp381411 жыл бұрын

    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.

  • @science-bite-size
    @science-bite-size11 жыл бұрын

    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.

  • @Dyenosoreusrex
    @Dyenosoreusrex11 жыл бұрын

    Oh thanks for clearing it up.

  • @hahaLOLimlaughing
    @hahaLOLimlaughing11 жыл бұрын

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

  • @uniramia4
    @uniramia410 жыл бұрын

    great video!

  • @shirlann9899
    @shirlann989911 жыл бұрын

    THX, the video was very informative.

  • @Mckreelove
    @Mckreelove11 жыл бұрын

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

  • @MartinaYow
    @MartinaYow6 жыл бұрын

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

  • @tshililomulaudzi6571
    @tshililomulaudzi65713 ай бұрын

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

  • @haleywunderlich2313
    @haleywunderlich231311 жыл бұрын

    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

  • @amasian16
    @amasian1611 жыл бұрын

    This is super helpful! T hank you!!

  • @Educationbanglaa
    @Educationbanglaa2 жыл бұрын

    THANK YOU very much . Love from India EASILY UNDERSTOOD

  • @UntilWeGotCaught
    @UntilWeGotCaught10 жыл бұрын

    Thank you so much! God Bless

  • @bouclesbrillantes127
    @bouclesbrillantes1272 жыл бұрын

    Thank you 😊

  • @avani3510
    @avani35106 жыл бұрын

    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

  • @emilywexler9238
    @emilywexler923811 жыл бұрын

    Works fine on my end. Great videos :)

  • @lil_lady8403
    @lil_lady84038 жыл бұрын

    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)?

  • @NeuroCurieux
    @NeuroCurieux3 жыл бұрын

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

  • @deepthireddyvasi2075
    @deepthireddyvasi20759 жыл бұрын

    was a wholesome vid indeed.

  • @BubblesandCake
    @BubblesandCake11 жыл бұрын

    You are my hero.

  • @MrPrabhubct
    @MrPrabhubct11 жыл бұрын

    Nice. Thanks.

  • @silencedidgood
    @silencedidgood11 жыл бұрын

    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.

  • @divermike8943
    @divermike89434 жыл бұрын

    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.

  • @frankieroandMCR
    @frankieroandMCR8 жыл бұрын

    better than my university lecturers!

  • @DIANA4972
    @DIANA49729 жыл бұрын

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

  • @bevanlouis5646
    @bevanlouis56467 жыл бұрын

    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

    @coordenacaobiologiaufpr296

    7 жыл бұрын

    I have the same question

  • @ernestturner2415
    @ernestturner241511 жыл бұрын

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

  • @cluelessdevice787
    @cluelessdevice78710 жыл бұрын

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

  • @lovelyfrenzy1
    @lovelyfrenzy111 жыл бұрын

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

  • @rodgersotokoma8289
    @rodgersotokoma82898 жыл бұрын

    Awesome..

  • @kimberlykv4313
    @kimberlykv43135 жыл бұрын

    How do you determine how many deaths there is?

  • @adiverma4712
    @adiverma47126 жыл бұрын

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

  • @GDonPadlan
    @GDonPadlan10 жыл бұрын

    Greetings Mr. Millard's H Biology class!

  • @Galaxy95311
    @Galaxy953118 жыл бұрын

    I love u so much thank you

  • @aumnamahshivaya6086
    @aumnamahshivaya60863 жыл бұрын

    Tq🙏

  • @simplebio7489
    @simplebio74892 жыл бұрын

    Super

  • @1farhinmomtazriana25
    @1farhinmomtazriana255 жыл бұрын

    Thanks a lot Sir. It was really helpful.

  • @davidschwarz2530
    @davidschwarz253011 жыл бұрын

    Video and sound work for me ~ David S

  • @AlwaysLoudAA
    @AlwaysLoudAA11 жыл бұрын

    Hello Mrs.Husinga class!

  • @EllyKSaysHi
    @EllyKSaysHi11 жыл бұрын

    is limits only related to calculus?

  • @silentbitbeadly8652
    @silentbitbeadly865210 жыл бұрын

    Tanks

  • @nat_han
    @nat_han7 жыл бұрын

    Glad they're only virtual rabbits

  • @CelineJennings
    @CelineJennings7 жыл бұрын

    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

    @leticiamartinez9373

    7 жыл бұрын

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

  • @divermike8943

    @divermike8943

    4 жыл бұрын

    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

  • @gold_lychee
    @gold_lychee3 жыл бұрын

    omg thank you

  • @uhlicawu
    @uhlicawu11 жыл бұрын

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

  • @mervonium
    @mervonium11 жыл бұрын

    Reminds me of compound interest

  • @fairyqueen4143
    @fairyqueen41439 ай бұрын

    Wow

  • @troybrinson19
    @troybrinson1910 жыл бұрын

    Ok sir

  • @markdonaj264
    @markdonaj2644 жыл бұрын

    Mr Folsom?

  • @evanshui4653
    @evanshui46539 жыл бұрын

    Linton sent me here.

  • @casss320
    @casss3206 жыл бұрын

    Bless you. Please teach my ap bio class.

  • @stephendelacruzone
    @stephendelacruzone3 жыл бұрын

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

  • @xdustymanx
    @xdustymanx5 жыл бұрын

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

  • @elizabethcrawford9356
    @elizabethcrawford93569 жыл бұрын

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

  • @Mornys

    @Mornys

    8 жыл бұрын

    +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

    @hannahshaler2101

    5 жыл бұрын

    elizabeth crawford you would round to 4

  • @xiiixiiih.16
    @xiiixiiih.16 Жыл бұрын

    💡🍎✌️

  • @Dyenosoreusrex
    @Dyenosoreusrex11 жыл бұрын

    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?

  • @iammichelewithonel
    @iammichelewithonel10 жыл бұрын

    They're just virtual rabbits hahahaha

  • @zoharwolfson8914
    @zoharwolfson89147 жыл бұрын

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

  • @sj.shewolf8435

    @sj.shewolf8435

    7 жыл бұрын

    Zo Wo I have accelerated algebra 😲😖

  • @kevinlam1828
    @kevinlam18287 жыл бұрын

    roooney

  • @carloemanueledoria7648
    @carloemanueledoria76485 жыл бұрын

    tseries favorite video

  • @xtourmaline
    @xtourmaline3 жыл бұрын

    they’re just virtual rabbits..

  • @michaelseanchang
    @michaelseanchang9 жыл бұрын

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

  • @shelleywell1

    @shelleywell1

    8 жыл бұрын

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

  • @shelleywell1

    @shelleywell1

    8 жыл бұрын

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

  • @buda1841

    @buda1841

    6 жыл бұрын

    realy????????

  • @buda1841

    @buda1841

    6 жыл бұрын

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

  • @CrazyGamer-xi8rf

    @CrazyGamer-xi8rf

    6 жыл бұрын

    Tell that to the Australians

  • @agdoombagdoom8540
    @agdoombagdoom85403 жыл бұрын

    There are just virtual rabbits 😊

  • @mervonium
    @mervonium11 жыл бұрын

    This formula re,i

  • @milaguzc
    @milaguzc8 жыл бұрын

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

  • @norapatriciamejia
    @norapatriciamejia3 жыл бұрын

    🐇 🔥 = 😢

  • @chrismedbury2049
    @chrismedbury20497 жыл бұрын

    i hate tis crap but I gotta larn it lmao