Evaluating and Graphing Exponential Functions

We know about functions where exponents are raised to different variables, to produce quadratics, cubics, quartics, and so forth. But what about when the variable itself is an exponent? This is called an exponential function, and they are important for modeling things like population growth and other real-world scenarios. Let's learn about them!
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[@tasmanager3530]

very helpful but i still hate math

[@Tusharplays69]

I'm in 7th grade rn from Bangladesh and i have none of this in my syllabus (they're just teaching basic multiplication and division of polynomials, and i've not even been introduced to pythagorean theorem in school yet.), yet i've completed almost a half of this series. And soon i'll get to learn trigonometry from your series, which is nowadays here taught in 9-10th grade. Thanks a lot to you professor because of you my parents aren't regretting paying wifi bills. ❤

[@Tusharplays69]

I'm not sure i'll be able to complete calculus because that is a bit over for me since it's here taught in 11th grade, but if i get time i'll definitely try to.

[@vital_vitamins]

good luck!!

[@twopolaar599]

Thats incredible! Here I am in 9th finding videos for this since I missed my classes, Im sure it will be helpful for you to learn this earlier.

[@Happiness_aada]

Le me learning these concepts in 11th basics 💀

[@jamesferris2664]

You are a magical legend of a man who flattens the flat Earthers and helps me with my Algebra homework. Thank you, Professor Dave.

[@cheressacargill5077]

This video was the most helpful thing I have seen in a long time! I have a quiz on this stuff today and totally did not understand when to reflect across x / y axis and this video was so helpful, thank you!!

[@80milekyle70]

Great video Prof. Dave!

[@DenovoTutor]

Your videos are amazing! You inspired me to start my own Tutoring channel :)

[@alexrubio40]

Your tutoring is shit

[@alexrubio40]

Lmao

[@user-qx7hi4dq5b]

Wow that shows you how even a simple video can affect someones whole life..

[@lvrhees]

Thank you so much omg your the only one who explains it where I understand

[@joelortiz9281]

I like doing exponential functions, but sometimes I struggle a little, sometimes I get it right. What I get It More right is the Chart with Numbers with power, like for instance, 3 to the -3rd Power, and I can figure it out as I understand.

[@masongarofalo9370]

Professor Dave explains is the best intro on yt

[@v.llafatechristie1429]

GREAT JOB PROF

[@Tudpxyz]

Thanks
Keep it up.

[@ahmedmazher3747]

Y = -2 ^ x
If x is even y is positive
If y is odd y is negative
How to graph it or i misunderstood some thing

[@melodyofsoul_]

I think he wanted to say Y = -(2 ^ x ) when he was explaining the graphs, the base must be bigger than 0 (in this example base is 2), as he mentioned at the beginning (1:23)

[@key63727]

how do you know what the horizontal asymtipbe is

[@Kai26448]

Thx dear

[@worshipcollaborative]

thanks bro

[@attaullah4005]

Sir g tose great ho

[@amishaparmar2413]

How can the graph of a>1 and b

[@adhiyanthaprabhujeyashanka2091]

Same doubt

[@e.m.o3467]

It should dip down to the left

[@heysharty2321]

if you have for example 4 as a and b is -x then you could for example plug in 2 for x so you would get 4^-2 since its to the power of negative x.
The function is actually like this f(2)=(4)^-(2). You just plug in the x value but that minus sign doesn't change

[@RadoHudran]

What I didn't get at first was him saying at 1:25 Base a must be positive.
Then later he says at 4:30 that you can put a negative sign there for reflection acroos x-axis.
I think i just means that (-3)^x is not an exponential function while -3^x is

[@kundanagarwal3563]

Yeah its true
(-a)^x {where a is positive number} is not defined

[@R4264S]

I had the same query !

[@Ramonoemoganedi]

When we now move away from x=0 to the largest negative values of x like x -1or x -2 provided y=3/4 or y = 1/2 how to plot the graph.

[@tGoldenPhoenix]

Done.

[@priencessme6100]

Idk anything abt em 😂😂 I draw this graphs easily by different method however thanks sur because of you I got full marks in exam told u abt it yesterday ryt? Ur my own teacher 😂😂 where r u from ,ur so talented ..my frnds said that you've studied tht much that u can get mad easily so sorry if u feel bad really how old r u ? How much years does it takes you to reach here hope you'll reply me by honesty

[@armandplays4355]

what

[@RadoHudran]

In what country do you speak like that xD

[@lilibethcervantes2161]

hi

[@santhoshmouli7442]

Hi Dave
I have small doubt
In the middle of your explanation
You say that a(base)0 the function will Dip down to the right , i understand this as per exponential function y=(1/2)to the x
But you also say a(base)>1 and b(exponent)1 and exponent is

[@santhoshmouli7442]

Now I get clarified

[@eggzed5499]

Ik I’m probably too late to comment this, but 2 to the x power has an exponent >0

[@user-mv3zf1cm6c]

W

[@dar5632]

Wild

[@OkSid300]

I've got to go on note here! The rational functions were my least favorite! They are as ugly as the fractions that produce them!

[@trisha5079]

jesus math