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07 - What is an Exponential Function? (Exponential Growth, Decay & Graphing). 

Math and Science
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In this lesson, you will learn about the exponential function and its applications in math, science, and engineering. The exponential function is very simply a base raised to an exponent. The value of the base determines the shape of the graph of the exponential curve.
Exponential growth occurs when the base is greater than one. Exponential decay occurs when the value of the base is between zero and one. The base isn't allowed to be less then zero in an exponential function.
In this lesson we will graph the exponential function and discuss the shape of the curve. We will learn when the graph represents exponential growth and when it implies decay. We will also discuss applications of the exponential function in all branches of science, math, and engineering.

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15 июл 2024

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Комментарии : 241   
@robertmulback6239
@robertmulback6239 4 года назад
You are a fantastic teacher I’m 75 years old studying math I went to college for a while but it’s been a while so I’ve been looking through your mathematics you’re really good at what you do I’m very proud of you
@MathAndScience
@MathAndScience 4 года назад
Wow thank you so much - your comment means a lot to me! Thank you again!
@sirousmohseni4
@sirousmohseni4 3 года назад
Hi Robert, I thought I am one of a kind to study math at higher age. Your comment made my day and made me more focused. Thanks
@johnrutland5663
@johnrutland5663 2 года назад
I'm almost 75 , a 8th grader with some college courses later in life and a math lover . Absolutely love your teaching . You're dedicated to teaching and gotta be a genius mathematician
@jackflash8756
@jackflash8756 Год назад
I'm 64 and now learning something new from this fantastic teacher every day.
@headbuttsforphaticcommunio3731
Maths not 'math'. Mathematics is in the plural. Americans can't speak English.
@gedesangging112
@gedesangging112 Год назад
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@avidrationalist7281
@avidrationalist7281 3 года назад
He is proving that someone doesn't need to be genius to understand mathematics, but an HONEST LISTENER. When you have a teacher of this nature, you just need to listen, and you are through..what a fantastic teacher..❤👌
@avidrationalist7281
@avidrationalist7281 3 года назад
He is not just teaching, he is demonstrating the BEAUTY OF MATHEMATICS...mind blowing teaching skills. 💖😍
@taleishaadams6899
@taleishaadams6899 5 месяцев назад
Was excellent at math until I had a seizure years ago. It wasn't until I returned to college recently, I realized how much memory was lost of my favorite subject. I have to relearn everything, but many teachers and tutors nowadays don't have the patience or lack the passion to thoroughly explain the subject. That is what I'm needing. Because of the quality in your videos, I have been able to relearn and retain. You are a true blessing and excellent at what you do. Thank you so much!
@jackiejarrell1335
@jackiejarrell1335 3 года назад
i enjoy your videos.... im 57 em learning algebra to help my grandchildren with home schooling during covid ! 2021
@milinda2569
@milinda2569 3 года назад
That's great!
@ssaha2749
@ssaha2749 3 года назад
Explained indepth of exponential function, thanks
@PrintPranav
@PrintPranav 2 года назад
@@ssaha2749 GREAT lol
@mufakkirhussain2816
@mufakkirhussain2816 4 года назад
Your videos are so interesting that I didn't even realize that how much time has passed
@omransaeed1988
@omransaeed1988 3 года назад
This is so true, oh my god.
@manuelfcasas3472
@manuelfcasas3472 3 года назад
A delight of explanation! I am an engineer, 56 years old, and really struggled with math courses when I was at collegue. There were few books available explaining the subject: many were very confusing, others a bit less. Being able to go over these videos, hit pause at a point, go back, as many times as you want, is something someone trying to grasp key math concepts nowadays should not take for granted. There were times when studying was much more complicated and much less delightful.
@aaaaii6511
@aaaaii6511 2 года назад
Im glad im not the only one.
@aaaaii6511
@aaaaii6511 2 года назад
Nobody elses time or money on having to pay a teacher or have to use their time. I can can go over, and I don't have to feed this virtual teachers or wait for restroom brakes. Its simultaneous that my peers at age 18 don't take advantage of this is time saving and free. I feel as if the future when you are gone and all is taking a turn where an oligarchy happens and people go to be extremely poor and only the rich will have more and more because they worked for it. At the same time. I do not pity those who do not want to experience all aspects of life.
@shawnd.8498
@shawnd.8498 2 года назад
Math can be fun if you grasp the concepts and terminology.
@ezraallen1550
@ezraallen1550 Месяц назад
4 Years old and still useful! I'm definitely coming back to this video for reference.
@MC-em7mu
@MC-em7mu 3 года назад
Thank you so much, sir! This have been a really great help! I didn't even realize it's 45 minutes long. You made math sound really fun and interesting here, it's never boring to watch! Well done!
@jeaniebee.
@jeaniebee. 3 года назад
Thanks a lot! My Algebra 1 teacher barely knows how to explain anything so I was left confused but after watching this video I understand quite a bit.
@johnmaulkin-ur8lm
@johnmaulkin-ur8lm Год назад
Just fantastic; I am 85 and hated math at school thanks to the ‘Christian Brothers’! How different it would be if I had had a teacher like you. Thank you.
@alyaspreetam5413
@alyaspreetam5413 2 месяца назад
I am 68 years old and Electrical Engineer by profession and Mathematics is my favourite subject. You demonstration skills are marvellous and has broaden my Concept at the grassroots level. You are a teacher of high caliber and hit/ awake the sleeping cells of mind very gently, and charge them basic original ideas for excellent concept clearance. I am so proud of you. I would like to request you to upload your videos on probabilits/ Permutations & Combinations . Thanks and God bless you.
@MathAndScience
@MathAndScience 2 месяца назад
Wow thank you!!
@ryanhayes5475
@ryanhayes5475 2 года назад
Awesome treatise to the most important function in math. Teaching Algebra 2 this year and will definitely be using this as a source of inspiration. Thank you for making this!
@antoniors
@antoniors 3 года назад
For the guys who do not understand why when 0 < b < 1 works in the way it does is just because when we have a fraction on the negative power we can always transform it to an integer with positive power. This is true for all exponents - x^-1 = 1/x and (1/x)^-1 = x^1. Example - 3 ^ -1 = 1/3^1 and (1/3)^-1 = 3^1
@lentonlawrence
@lentonlawrence Год назад
Some maths teachers send shivers down their students' spines. But this teacher dosen't just makes the subject enjoyable, he breaks it down for laymen to understand it. This is demystification of mathematics at its best !
@mrkylejaypadilla2563
@mrkylejaypadilla2563 2 года назад
PERFECT EXPLANATION! Application and Real-life situation scenes. He talks at the right speed.
@goriolaganiu403
@goriolaganiu403 3 года назад
Am very happy to have met you.Your explanation is always supported with common sense which many of us need for pure understanding
@ishanac
@ishanac 3 года назад
thank you so much! I'm studying for the SAT and this helped me a lot
@melsilva1940
@melsilva1940 2 года назад
me either
@stephensonal4082
@stephensonal4082 2 года назад
I like the way you put maths and science into context - you are a good teacher. Thank you for being you
@MathAndScience
@MathAndScience 2 года назад
Awww thanks!
@Devarati
@Devarati 2 года назад
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@priyankanajwa5111
@priyankanajwa5111 2 года назад
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@unzilaunzila3980
@unzilaunzila3980 2 года назад
A brilliant teacher of Mathematics 🧮
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@shaymaa8007 3 года назад
I kinda addicted your videos, you’re awesome
@jay22197
@jay22197 3 года назад
such an amazing instructor, makes you want to learn
@olajumokefamuyide9640
@olajumokefamuyide9640 2 года назад
I honestly can't thank you enough for this lesson.
@olgasantiago2033
@olgasantiago2033 2 года назад
You are the best teacher ever. Your explanation is marvelous ✨. Thank you so very much. I didn't know anything about exponential fuction but now I feel that I know everything about it 😌.
@ellafeng6087
@ellafeng6087 2 года назад
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@niceguy4801
@niceguy4801 3 года назад
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@binodk2561
@binodk2561 8 месяцев назад
Best Mathematics Teacher in the World... Amazing knowledge
@AbdurrahmanAllahem
@AbdurrahmanAllahem 4 года назад
Thank you. A great memory refreshing.
@Ahtohallan.
@Ahtohallan. 2 года назад
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@berhanekidane5572
@berhanekidane5572 Год назад
I found your way of teaching very impressive and your Lesson has been prepared in a simplified way.I had never been to any higher education in my Eritrea. I enjoyed your Math Lesson greatly.I am 80 years old.Thank you very much Sir.
@frankbrady1949
@frankbrady1949 3 года назад
My grandson's Algebra 1 (8th grade) course deals with exponential functions but his text doesn't have enough to increase his understanding of them. You're presentation provided that understanding. Thanks.
@leomcinston8667
@leomcinston8667 7 месяцев назад
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@Breazyy1
@Breazyy1 Год назад
Thank you for these videos man, you have helped me so much to understand functions. You sir are a legend!
@alexandregavaza3882
@alexandregavaza3882 3 года назад
Amazing teacher. We can feel your passion and you are able to get us confident. Never saw Math as something so easy but now I feel like should specialize on this amazing module. Congratulations...
@manojishere
@manojishere Год назад
Everything very beautifully explained.
@emekaosegbo37
@emekaosegbo37 11 месяцев назад
Your teaching method is great. I'm thrilled.
@moes.d6548
@moes.d6548 4 года назад
Thank you, excellent teacher!
@MrMossadiq
@MrMossadiq 2 года назад
Amazing. I enjoy to learn from him.
@patriciab1681
@patriciab1681 Год назад
Nice and refreshing to learn in simplified explanations thank you
@binodnepal2715
@binodnepal2715 Год назад
Profound lessons. Keep it up. Recommend everyone
@Rasha.Hussein44
@Rasha.Hussein44 Год назад
I watch all your videos they are helping me for the SAT
@yafy.5158
@yafy.5158 4 года назад
you are the greatest Teacher ever!
@roysmith3198
@roysmith3198 3 года назад
I agree. He teaches why more than how, that is the biggest advantage when learning. I only watched about 3 of his videos and he became my favorite.
@dayanandetubone9077
@dayanandetubone9077 3 года назад
Thanku sir, this is what I am learning real maths.its very interesting.
@user-dh3tr5lu1k
@user-dh3tr5lu1k 2 года назад
Hello as a 9th grader who wants to study physics and mathematics these videos are very helpful. Thank you!
@enlightenedindia6428
@enlightenedindia6428 Год назад
Simply great greatly simple and loveable
@ariturbo4094
@ariturbo4094 2 года назад
Great mentoring ,,,,, deep respect,,,, you have beautiful handwriting Sir
@swadeshtaneja3512
@swadeshtaneja3512 3 года назад
If some hits dislike button for such awesome lectures then I request them to give the reason also so that we know what is wrong with the lecture..Is it the content or presentation?
@navindraarjunaabeyesekera7864
@navindraarjunaabeyesekera7864 2 года назад
Yes . You are a Good Teacher
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@attiaali3813 Год назад
Fantastic Teacher!
@so-rendom
@so-rendom 3 месяца назад
I was Preparing for iit jee and his videos helped me alot and now I'm an iitian ❤️❤️
@devnshugarg6255
@devnshugarg6255 3 года назад
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@florentinosanchez3969
@florentinosanchez3969 4 месяца назад
You are the best teacher!!!
@user-su4ex2ps6q
@user-su4ex2ps6q 8 месяцев назад
I enjoy your teaching tutor and I hope and i hope i will understand this topic more than other topics
@gautamroychoudhury2735
@gautamroychoudhury2735 Месяц назад
You are an wonderful teacher.
@Cheesecakeriver
@Cheesecakeriver 5 месяцев назад
i'm currrently getting ready for a math exam, then I can start studying abroad! and your video is AMAZING. Thanks 🩷🩷🩷
@johnroberts7529
@johnroberts7529 Год назад
Wow! What a great lesson; a real pleasure to watch and listen to. Thank you so much for the all the hard work that you must have made to put it together. When you 'went' negative that really caught my attention. (-2) ^X for instance... there must be discontinuities on the graph eg (-2)^0.5.
@erinhefferin859
@erinhefferin859 3 года назад
Thank you for this.
@w0mblemania
@w0mblemania 2 года назад
This is an excellent video. Thank.
@iariiarina9580
@iariiarina9580 3 года назад
Thank you so much for this video!
@Dk-hh4sl
@Dk-hh4sl 2 года назад
I echo others comments. You are a fantastic teacher. I wish i could have you as my teacher in school.... thanks !
@Rasha.Hussein44
@Rasha.Hussein44 Год назад
BEST MATH TEACHER EVER !!!
@alialameer7553
@alialameer7553 2 года назад
Great teacher, thank you
@felixyongco4420
@felixyongco4420 Год назад
He is such an amazing Maths Tutor. I have learnt esp. f ( x ) = ( - 2. ) ^ x is. impossible .. because the raising on the value of X goes haywire..esp raising to. odd number for the power VALUE of X . Thanks Sir Jason.. very clear instruction and highly eduvational video..
@RahulSingh-fk8dh
@RahulSingh-fk8dh 2 года назад
Thanks for the explanation
@philipjohn1338
@philipjohn1338 7 месяцев назад
Master of teaching
@Aminhelal210
@Aminhelal210 2 года назад
You are a great teacher
@victorsanchez-wg1rz
@victorsanchez-wg1rz 3 года назад
GRACIAS MIL POR LA PESENTACION...SALUDOS DESDEEL REINO DE LOS KITUS (Quito-Ecuador)
@sallaklamhayyen9876
@sallaklamhayyen9876 3 года назад
brilliant explanation = brilliant teacher = thank you son much
@gulshanbibip3687
@gulshanbibip3687 Год назад
You are amazing teacher
@maleeshapriyanjana7604
@maleeshapriyanjana7604 2 месяца назад
Great great help!
@marijana128
@marijana128 6 месяцев назад
you never disappoint
@briannyirenda5924
@briannyirenda5924 Год назад
I do enjoy your teaching
@Ilovegojosm
@Ilovegojosm 10 месяцев назад
افضل من دكتورتنا 🫂
@hazelchong5111
@hazelchong5111 2 года назад
watching your vids make me a better teacher
@SsLoage
@SsLoage 2 года назад
AHHHH THANK YOU I LEARNED SO MUCH I hope i can pass my algebra😭💖💖💖
@remanbist3622
@remanbist3622 3 года назад
thank you so much sir much love!!
@mahendarreddykura6250
@mahendarreddykura6250 3 года назад
Nice explanation 👌🏾
@larysamakar9333
@larysamakar9333 4 года назад
Love from Norway!
@SirAtticus
@SirAtticus 3 года назад
best teacher in the world
@nynmlg2299
@nynmlg2299 2 года назад
No one in Germany explains it so good! Thank you sir
@bilalbakoleismail5324
@bilalbakoleismail5324 7 месяцев назад
A perfect teacher
@jay_wright_thats_right
@jay_wright_thats_right 5 месяцев назад
I really like this man.
@Mikael97
@Mikael97 3 года назад
Great lesson sir, I am 23, I didn’t learn exponential function in high school, but now you made it clear to me,I am watching your lesson from 🇧🇷, I enjoys it,anyway thanks a lot.
@Ahtohallan.
@Ahtohallan. 2 года назад
What are you watching it for? Sorry just curious
@Mikael97
@Mikael97 2 года назад
@@Ahtohallan. I work in a Bank, we use it exponential function to define interest rate on loans
@Ahtohallan.
@Ahtohallan. 2 года назад
@@Mikael97 ah cool cool. Have a good day :)
@zuko7465
@zuko7465 3 года назад
I realle like it. Thanks a lot!!!
@jkgan4952
@jkgan4952 3 года назад
Thank you so much!
@mahipalratheerohtak7956
@mahipalratheerohtak7956 Год назад
A teacher with subject knowledge
@phugoid
@phugoid 2 года назад
Lovely lesson. I just wish you'd explained what the actual implication of a fractional base, viz. an exponential depletion of whatever it is that we're calculating for. For countries with a population growth rate of under 1, the implications for the future should be obvious
@paulbany6603
@paulbany6603 4 года назад
Well done
@thethreepariahs5579
@thethreepariahs5579 3 года назад
perfectly explained.
@scarlet0017
@scarlet0017 Год назад
Thank you so much
@ariturbo4094
@ariturbo4094 2 года назад
I m starting to become tutor in math as for my retirement job,,,, going back to this math tutorial is like refreshment after 28 yrs leaving university
@johnallenadriano540
@johnallenadriano540 3 года назад
Thank you!!!
@aaniyahchetty402
@aaniyahchetty402 Год назад
Thank you so so much😊
@tresajessygeorge210
@tresajessygeorge210 9 месяцев назад
THANK YOU... SIR...!!!
@lucasgweru3
@lucasgweru3 Год назад
You are a hero
@piyushjha1892
@piyushjha1892 4 года назад
Ty Sir from India 😍
@user-oc4bm5hr9x
@user-oc4bm5hr9x 11 месяцев назад
Awsome teacher
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