Exponential Decay / Finding Half Life 

Thanks so much, these videos you put up are not in vain. Students enjoy someone who is willing to teach us without pay. What amazes me is the fact that you do this out of your time to help anyone who needs help with math. Thankyou Patrick!!!

*ad* : are the videos from 2006 really heloing? me: YES

boo ya! i always count the number of left handed people in my classes...

Very very helpful, thank you! Also, the bracket at 4:00 is a work of calligraphy, bravo! Mine are rubbish.

Great job of explaining decay. Might call it an isotope to be more correct.

There are a lot of left handed math tutors on youtube.

Our teacher showed us a different way, but this is much easier, I hope he accepts this method on the test. Thanks, you rock and keep up the good work!

your method is so much easier than y(t)=y(0)e^kt

@saifirefly well, exponentials would be taught in any algebra class

@wen2669 lol

Would you mind making a video with one of these problems using the N(t)=N(initial)*e^rt version of the equation? My instructor is picky with how we solve the problems. Great video though! At the least I can use the answer as a reference to verify I'm doing things properly.

no problem mr. nick-bucket!

@MechInvent my name is not youtube

Thanks you so much dear professor for precise formula.

@Jmerino7 there is no calculus in this video

Thanks so much for this! I missed a week of school and came back on a test day. I learned the entirety of the material with just two of your videos. Thanks, man.

you are not multiplying in either case. and it does not matter what base you use.

@aka7minimouse it just sounds like your teacher is trying to make some systematic procedure for people to follow.

Half Life 3 never came out

My professor is using a different process and I'm lost. She's using Qbase0 e^-kt. She didn't explain. It's with chapter of Logarthmic Functions if that helps any. I'm assuming in later converts into the natural logarithms you have here. Is there an example you can show me for this? Question looks like: (Find the associated exponential decay or growth model) Q=1000 when t=0 and half-life =1. Another Question: Find half-life or doubling time when Q=1000e^0.5t Please help math genius!!

@duckhero3 let a = some amount, let y = half of that amount, solve for t.

@VerifiablyNoticible put a math term in the search as well next time : )

What about finding the rate of decay of a half life if, for example, its 400 years

@lmaominh sorry to hear that. my 8th grade science teacher, mr cox (now there is a name you can make fun of) told me i was a nerd cause i knew the answer to one of his questions. lots of weird people out there, teachers included.

So for finding any half-life, couldn't we just start with: ln (1/2) / ln (1+(constant annual decay rate)) = t And just plug in the constant annual decay rate?

i spend money to not learn this in college and learn it on youtube for free! Thanks dude!

how do I solve for the annual decay rate if I'm given just only the half life which is 22 years, what do I do or how do I solve it?

If I could be granted one wish, I would wish for PatrickJMT to teach at my school because he's a very effective teacher--very easily understood! KUDOS! :)

Man you are leading me through college. Thank you for your videos!

So just wondering, what is the difference between this formula that you teach, and A = Pe^rt? Are they the same? Or if not, under what circumstances would you use each equation? Thanks for the help!

@KittyKatCurls this is annual decay rate; you are using the formula for continuous decay rate

@patrickJMT its okay people call me fresno lol

you are an excellent teacher but this Half-Life method is seeming to confusing for me. my teacher shows us a chart method whree you have 3 rows in the chart. Number of half lifes/Time elasped/Amt. remaining. Do you know this method?

@Stairs3000 he's the Patrick of math.

thank you for the awesome job u do via the channel. don't wait to much in getting ur phd since having u as a university teacher would be great, because u know how to explain math very well and thats what we need in our schools. thank u n don't stop making this math videos

Hey Due u are the secret of my success in math thanks

carbon 14 has a half year of 5730years an initial sample has a mass of 70mg, how much is left after 171900 years? how many half lives have gone? what is the mass of the daughter isotope?

i don't get it. isn't this too easy to be calculus? it is in your second semester calc playlist but i don't see any derivatives or integrals used to solve these.

thank you! o A o but uhmm caan i ask....do you use LOG with half-life? the formula my teacher gave us is A=Ao(1/2)^t/h A= amount left after given time T=Time h= half life Ao=initial amount o 3 o

our generation have it way too easy too learn but its easier to be distractied on the internet

why do you multiply the equation by LN and not by Log? My teacher taught me that when you have an exponential equation with different bases you can multiply by log, so i don't know when i should multiply by Ln or Log.

what if its decreasing every 7 years, where would plug that in?

trying to look up half life related tutorials on youtube = searching through endless videos of Half Life (The video game...)

Hi patrickJMT! Why use Natural logarithm instead of Common logarithm? Thanks for the video tho. :)

i would ask first! sometimes, it is about the process - not about the actual answer (well of course, the answer is important, but they are trying to teach a process in algebra class). your instructor may be trying to emphasize something that this procedure leaves out ! (not sure what it would be, but again, i would ask to make sure)

I got lost at the natural logarithm part....why did you have to use it and how did you get those numbers? (- .693147 / - .040822)???

So can anyone help me with a problem? I take a dosage of something every 24 hours, and the drug has a half life of 20 hours, how would I find out how much is in my system after x hours? I don't know how to handle it because I'm not just taking the initial amount, but I'd be topping up every 24 hours.

@yeijie456 the formula you have is for a CONTINUOUS decay rate, mine is for ANNUAL. those two words should be key words to help you decide which formula to use. :) ask your teacher for some clarification if you are not sure!

What if the constant annual rate is a number bigger than 1? Making it a negative result and if I'm correct (unlikely) then I can't use logarithms.

Why is it divided by 100 at 3:10 is it cause 100 is the highest number or because it's an easy number to throw out there??? Pls help asap

I am really confused, my problems that our teacher taught we use y=Ce^xt Why is it that there is no e in the formulas you used for this video ?

Thanks so much, these videos you put up are not in vain. Students enjoy someone who is willing to teach us without pay. What amazes me is the fact that you do this out of your time to help anyone who needs help with math. Thankyou Patrick!!!

our teacher did`nt show us by log method this seems easy but we havent studied log yet she showed us by dividing 100 by 2 then continuing

Awesome explanation. Thks!

Also, when I calculated it, 10+20+40+80+160+320+640=1270 and ur answer is 1280 do I have a mistake in calculating??

Is the method pe^rt very good? where p is the number that we start with and r is the rate and t is the years....

Well, part of this is right. He forgot that when you use natural logarithms you must write your equation using in the proper form using e. He should have been using log base 10 for the form he used.

is anyone else having problems with the video? it stops loading in less than the first minute..

Me a calculus student who isnt even taking chemistry 😭😭😭😭

please dont say LN please say natural log. it encourages us to use college math words

PLS HELP WHEN I PLAY HALF LIFE WARZONE THE GUY THAT HAS TO OPEN THE DOORS FOR U WON'T COME :((( HHHHHEEEELLLLPPPPP PPPPLLLLLSSSS

hello this vid helped me super mucho but have a conflicting issue on how to connect that into this problem: radioactive iodine decays accorindg to the equation y=ae^-0.0856t where t=days...how should i find the half life here? is the percentage decay 8.56%? nd then go from there likeyour vid?

I'm stuck , why does my math teacher always tell me to do 0.5 = 1e^kt ?

Ok, I think I actually get it now. there's an r in both formulas, y=a(1+r)^t and y=ae^(rt), and they're BOTH growth/decay rates....BUT if you put the same number "r" in both formulas, you get (slightly) different functions. So, that's why you look for the word "annual" (or some other fixed unit, like "daily" or "hourly") , or "continuous", before the words "growth/decay rate". "Annual" tells you to use y=ab^t (or y=a(1+r)^t ) "Continuous" tells you to use y=ae^(rt).

My chemistry teacher makes us use k(rate constant)=.693/t 1/2(half life). So the problem you showed in this video was "what is the half life", but what if it asked for like the remaining on a substance or how old is it? then what formula do you use? My chemistry teacher makes us use this one: Ln(natural log) Nt(remaining) / No(initial mass) = -Kt

Thanks Bro... Thumbs Up... I Hope You're my Professor in my Mathematics subjects.. tsk..

My final sample exam has this problem on it: You have a radioactive material which decayed by 20% in one hour. By which percentage will the material decay in 2 hours? How exactly would I go about doing this? Is it as simple as it sounds or is there more to it? I may have figured it out simply with a ratio problem using this formula(excluding the variable A and making y=x^2), getting 11% as the answer, but I do not think that is correct.

im confused to what deos ln mean? sry im only in physical science!

Half-Life 3 confirmed.

hey thanks Patrick a lot man I m also left hand man some genius like you .me too I'm also genius man .you are not the only one but the way you are good really and i appreciate you intelligent in math but me is math and applied math both .i 'm engineers too . keep well man and keep doing that to help people and god blase you

This still confuses me as well. Why wouldn't y=Ce^(k t) and y=Cb^t give you the same equation, just with b=e^k? Are they actual different situations or just different ways of finding the same thing? Please help :)

I still don't get it, if half life = the amount of time for a substance to get to half of it's original start, and in this problem it's is decaying a constant anual rate of 4% we want to get find out how many years will it take that 4% to equal 50% or 1/2... Why not just make it 4X = 50 in which x represents the years and 50 is the amount lost after completing one half life (100g/2), then I get 12.5 years as the "half life", what am I doing wrong, I know the formula and how to solve it, I just don't understand why it works, plz help

you can use either one In- natural log log- base log so you would the reason why he uses In instead of log is because it is easier to work with..so... yh that's the reason!!

I have a question. My pre-calc teacher never really taught us logs and ln so I'm now I calc and lost beyond belief. Your example helped but what else is out there?

Hey Patrick. Do you have any videos on continuous growth/decay rate. I am learning exponential growth and decay but with the formula, y(t)=y0e^kt (y0 = y sub 0) Thanks a lot! if only my math teacher were as good as you!!!!

important!! for growth and decay, the formula my teacher gave me is A(sub t)=A(sub o)e^kt is there a difference? or is this a different formula alltogether

I’ve been trying to find videos to find what’s wrong with me, so I’m watching the half life calculus, because I am living half the life I should be living

thanks! might as well TRY to not fail a test, and now im 98% sure i wont fail this one XD

thanks so much my math teacher told us to learn and research this ahead so i know what we are going to be talking about tomorrow!

@arcstormtroo natural log. LN, look on the calculator

that help me so much. i was so stuck on my home work. thanks

10/10 your explanation is for some reason much easier to understand than others....

THANK YOU PATRICKJMT def showed me a flaw in a project i was about to hand in. Freakin life saver right here!

I use the rule that says N(t)=N0 e^rt but the one u used is more clear. Thank you thats really helpful.

"I like using numbers because they make more sense to poor Patrick" XD

Strontium-90 has a halflife of 29 years. If there are 400 grams of strontium-90 initially, how much, to the nearest gram, will remain after 87 years?

sir, can you explain the calculation of rate of decay with half-life given?

I'm trying to find the gram.... of the radioactive isotope.

I'm writing a test on Tuesday and you're saving my ass rn with these videos. thanks, man!

Your video really saved me today with my homework, thank you so much

Half life, full consequences

Is episode 3 hidden in this equation?

you saved my life. words cannot express how amazing you are!

@patrickJMT so does this meam i shouls solve it like 0.5a=ae^8.56t and then tjat would be ln0.5/ln8.56?

I keep on getting the wrong answer in the calculator 😑

Is this half life 3?????

Shouldn't it be a radioactive isotope, instead of ion?

what if the t has a fraction in it?

thanks youtube, for teaching me more than college does

o is the starting amount