Exponential Growth / Population Growth Problem.

[@Bee_Bill287]

Now I remember why I failed MATH.....

[@jamesdale8222]

Once he started saying the letters is when my brain broke

[@93deadpool]

Where did the 'p(t)=Ae kt' bullshit come from?

[@patrickjmt]

From a cow

[@adnanenewgate1492]

+patrickJMT from a bull to be more specific Haha

[@ijailbreakyourdevice8709]

patrickJMT I think you should be nice to us and tells us :) the

[@delahkful]

f(t)=Ae^kt

[@Azagro]

Standard differential equation. Where k is a constant and the exponent comes from the left hand integral of [initial condition, end condition], which gives you an ln(P)=kt+C therefore e^ln(P) = e^(kt+C) e^C = A P(t) = Ae^kt

[@dougaldmactaggart990]

There is a much easier way to do this. treat the initial 200 bacteria 3 days ago as your starting point. So we have 1000 bacteria = 200 bacteria x k ^ 2 days (because it took 2 days for the 1000 bacteria to grow from the 200 bacteria) Solve that equation for k = 0.34949 Than write another equation where t= 4 days because its 4 days after the initial 200 bacteria. so it would be: x bacteria = 200 bacteria x 0.34949 ^ 4 days Boom

[@alexisnguyen8081]

thank you so much! that is MUCH MUCH easier!

[@britniisar7833]

Is k a constant?

[@ellorichards]

how did you get 0.34949

[@lawrencefancelli1226]

Your left handedness is killing me!

[@marieplesco]

Lefties unite!

[@FrancisNtiFrimpong]

A different approach: Let 3 days ago (-3+3))= initial ie, 0  p(0)=200 e^(k(0))----- eqn 1 Let 1 day ago (-1+3))=2 p(2)=1000 e^(k(2))---- eqn 2 Also p(2)=200e^(k(2)) --- eqn 3  1000=200e^(k(2)) Solve for k to get k= (ln5)/2 Put value of k into p(t)=200 e^((ln5)/2(t))----- eqn 4 Solve to get p(t)=200 (sqrt 5)^t---- eqn 5 Let 1 day later (1+3)=4 So p(4) =200 (sqrt 5)^4= 5000

[@yunl1159]

Why is it not possible to set 3 days ago as the initial time t=0 and A (initial bacteria population) as 200 (bacteria that was present 3 days ago)

[@ggm15entertainment]

Dan L you definitely can. He solved in a more complicated way.

[@aphelelendovela]

Thank you so much for this video sir god bless you❤

[@Sotrass]

I am bored and searched for calculator bacteria and ended up here. I manage to learn things in the strangest ways.

[@melariemantanona2316]

Probably the only part of my exam tomorrow that I am dreading. Thank you!

[@MsBeatria]

I love you so much! To be frank. :) Patrick, thanks for solving most of my doubts.

[@kon1241]

I don't understand what happened around 3:00 how did you get the 1/ e2k

[@JR-iu8yl]

Dividing the numerator and denominator as well as using the law of indices

[@tamircohen1512]

For those who want to know where the formula comes from, unfortunately you need to know a little bit of calculus and how to solve separable differential equations. When the rate of population growth is proportional to it's size: dP/dt = kt, where k is a constant of proportionality. This is just simple direct proportion. When you solve this differential equation, you will end up with a general solution: P(t) = ae^(kt) where a and k and both constants to be found. This just means that the population size at any given time can be found using this function by plugging in a time. To find a and k, simply use the data you have been given to eliminate some terms so you can solve for the variables. Then plug in the time you are interested in for the question to find out the population at that time.

[@oshiozokhaiabu8068]

So, this video is meant for calc?

[@patrickjmt]

you can use the ' logistic equation ' - oddly enough, i have videos about this :)

[@jeremiahdeleon4923]

I'd rather do it this way: represent: 200 P(0) 1000 P(2) Find: Day 4 (current day) @P(2): solve for k 1000=200e^(k(2)) k=0.80472 @Day 4: P= 200e^(0.80472)(4) P= 5000

[@suvapillay9358]

Beautifully explained

[@tylerwebb7303]

Integration by parts can be used if you use dN/dt=kN (dN/dt representing the rate of change of the population with respect to time, and N representing the population size); This is the literal calculus translation of rate of population growth is proportional to the population; simply separate, and integrate (with respect to time) to get a formula for the population number at any given time.

[@MariaWiltscheck]

At ~4:20 you are simplify ((ln(5)/2) to ((ln(5) x 1/2). That makes sense. But then @ ~4:30 you take 5 and RAISE it to (1/2). Shouldn't you just be multiplying it by (1/2)?

[@oshiozokhaiabu8068]

I'm still so confused

[@mguven]

That was awesome. Thank you!

[@murillojessica23]

hey patrick quick question in other exponential growth rate problem you use p(r)^t and p(1+r)^t could you explain the Ae^KT any help much appreciated

[@carolinerozado7858]

this is super good. Thank you so much!!!!! Literally saving my Calc 2 grade :)

[@oshiozokhaiabu8068]

Yeah.. see.. this is too hard for Algebra II

[@sheamckenzie9956]

Thank you very much, good video.

[@patrickjmt]

@PeppermintPiano thanks for checking me out first ;)

[@paolo4709]

Thank You!

[@luizarthuraquino5745]

The logistic population growth model is described by an equation of the form P(t) = PL/(1 − ce−kt) , Where PL, c, and k > 0 are constants, and P(t) is the population at time t. PL represents the limiting value of the population since limt→∞ P(t) = PL. Use the census data for the years 1950, 1960, and 1970 listed in the table on page 105 to determine the constants PL, c, and k for a logistic growth model. Use the logistic model to predict the population of the United States in 1980 and in 2010, assuming t = 0 at 1950. Compare the 1980 prediction to the actual value. *Please Solve ?*

[@angrypepecancer5205]

What rule is when you divide the 2 equation together to cancel that variable (A initial)

[@lydiabergeron875]

Thank you SOOO much!!!

[@zapiroparen7778]

A bacteria culture which started at 2,000 became 6,000 after 4 hours. After how many hours will the bacteria reach 20,000? The amount of bacteria increases exponentially. is this still applicable to your given equation?

[@MrAlbashiri]

like always. you are the best ever :*

[@bhoylangis..5777]

Thanks for sharing god blees

[@wallybaldemor8523]

How many covid 19 cases after 1 year? Can we apply that?

[@gloystar]

I'm gonna prepare my disinfectant for tomorrow then.

[@DeeNieves]

i have to do a project for math and im kind of confused. i have to do the population of a country which in 2000 was about 6.2 million and it was growing about 2.1 percent and i have to figure out what the population will be in 50 years? I have no idea how to solve this? HELP!!!

[@glennrickelton4093]

If you work out the initial value as being square root of five X 1000 then we get a higher value than our other amounts - where am I going wrong?

[@ΧρυσοβαλαντηςΤασιοπουλος]

The set up is odd you should consider the case assuming that the population is given as a function of time P(t) so the rate of change is given by the notation dP/dt and we know that dP/dt =Kp(t) this is the first order diff equation solving it by integration both sides we get P(t)=Ae(exponent)kt+c initial conditions!

[@shaboatrad4066]

AWESIOME QUESTION AND AWESOME ANSWEING

[@ColeJT]

A population of Amoeba starts at 1000. An hour passes and the population reaches 2000 [with continuous growth.] After this time, 100 amoeba are continuously taken out. What is the population after three hours? I have that A' = A - 100 (since it's constantly doubling at a rate of (number of amoeba)/ hour then minus 100/hr. However, when I rewrite this as A'-A=-100 to set it up as a linear differential equation, find a multiple of integration U=e^([integral]-1dt) U=e^(-t)

[@TonyNguyen-it7vd]

Can I always assume K is constant? Assuming if I need to solve for two different time (t) intervals? (ex. year 1750-1800 then 1800-1950)

[@gerryy8724]

a culture of bacteria grows by 33% every hour. if you start with 3, how many will you have at the same time the following day? help me solve this problem please..

[@saturdaycookie]

Struggling with an equation. Suppose a colony of ants grows exponentially with a relative growth rate of 15% per day. On the first day (day 0) there are 60 ants. a. Write an exponential growth equation A(t)=Aoe^kt modeling this colony, where A(t) gives the number of ants on day t. b. On what day will the population of this colony reach 180 ants? Any help is appreciated! Thanks!

[@laurapaid9076]

how do I calculate to find the DAILY% when the populating doubles every 3 days?

[@johnnynguyen9770]

My hero.

[@LiveLaughLovee4Eva]

I was wondering if you can help me since even though i watched the video im kind of confused on this particular question. The question is: "The population of Barrie was 300,000 in 2003. The annual growth rate has been 6 1/2% per year since then. Determine the population in 2018" Also, Thanks soo much for posting videos you make everything so clear since my teacher doesn't teach us much

[@oshiozokhaiabu8068]

I hope you got help haha

[@lukasfraley]

I lay blocks for a living, but came up with 5000 by just looking at it and using common sense. 200 x5 equals 1000... so every 2 days is times 5. 1000 x 5 is 5000. duh.

[@breazfreind402]

yea this person didn't really show the actual application

[@ToadallyJon1]

According to my class and anything else I've read, for these k is always considered a constant

[@eldajean8938]

Where the video before this explain the equation?!?!?

[@emmamiracle344]

This guy is literally all over the place.

[@paulconnor9185]

(sqrt(5))^1=5? Doesn't it equal sqrt(5)?

[@Raindeux]

+Paul Connor He said sqrt(5)*1000*sqrt(5)^1. He combined the two square roots to make it 5*1000.

[@eldajean8938]

Why did you divide the two equations?!?

[@ccl8631]

helpful, thanks!

[@maiacamille96]

You're a wizard.

[@jo_10]

this is way too sophisticated.. the growth of bacteria is 500% from 3 days prior to 1 day prior so thats 5 times per 2 days therefote 2 days later the number of bacteria will be 1000 x 500% which is 5000

[@vetacoth]

There's no point in showing work. I looked at the problem and solved it in under 10 seconds. 200* x =1000 x=5 per 2 days 1 day ago + tomorrow=2 1000x5=5000. It's the work I don't know how to show.

[@learn_what_I_learn]

Save time man. Time is money. Do step jump.

[@breazfreind402]

this question didn't require the application of e. easy, 2 days x 5 is the answer so 1000 x 5 is 5000. could'a used a more relevant example sirey

[@emilyrawahi684]

thankes alot....

[@YingCaiProductions]

this made my brain explode. fucking kms

[@Violet.Bora_]

but why wasnt it 5 * 1/2 not 5 raised to the power 1/2. UGH

[@fanimeproductionst.v.3735]

It wasn't 5^1/2, it was e^ln(5)*1/2 His writing just makes it look like that.

[@nightfire4107]

My microbiology course have us doing this problem & it didn't mention any math course as prerequisite. Man I got confused.

[@walter8154]

is this calculus?

[@JR-iu8yl]

What do you think

[@oshiozokhaiabu8068]

@@JR-iu8yl Yes?

[@reksai2514]

Ok that's enough internet for today

[@zippy133713]

so much bacteria... i need to go wash my hands

[@einsteinyamat3894]

You can just use this geometric sequence thing... :>

[@r4microds]

is this 11U or im i seriously just seeing this kind of growth problem for the first time?

[@Xiaobooom1234]

why is -3, should be used for future not in the past

[@johnathanle7602]

What math is this so I'll know to avoid it.

[@sbk1398]

+Johnathan Le calculus :P

[@Raindeux]

+Samuel Kajah This is basic algebra.

[@ClumpypooCP]

Raindeux Yeah but the law of exponential growth comes from calculus, so most people doing this stuff are actually doing it for a calc class

[@mahdiashahid2007]

lol XD

[@RubiMercuri]

Precalc

[@ashleysoto5247]

Once he got to logarithms, I wanted to cry. I was already everywhere but the bomb dropped when he began to use them.....damn I don't know how I'm going to survive four more years of math...just to become a doctor....😣😣

[@MyCStudios]

this is now on the gcse syllabus- i don't know ANYONE who understands it! please help!!

[@oshiozokhaiabu8068]

I am so confused

[@anjurajpoot434]

That's So long plz simplifies this

[@lightsoutentertainmentdj]

doesn't matter man... sometimes you have to learn how to show your work.. and make it look all fancy for a grade in class.

[@nasradinali]

Great

[@joule-trix]

shouldn't it be 3??!??!?!?!?!?!?!?!?!?!???!?!?!

[@birdtweet1]

what a god

[@arctictern6198]

wrong if t=-1days one day later = t=0

[@danielberry777]

Left handed mfs are always the smartest

[@javedali6327]

p=600 r=500 t=2year

[@dallasbeus2117]

replace the bacteria with humans and you have over-population.

[@joshmetcalfphotography]

First 2020

[@coopercraig2462]

terrible job explaining, needlessly compilcated

[@oshiozokhaiabu8068]

Help