Exponential Growth and Decay Word Problems

[@montyscodmoddingservice74]

Thank you so much. I've been learning this for 2 weeks now at my high school, and I still didn't understand this. I was failing. But after just 6 minutes of watching your tutorial, it's starting to make sense. My grades have improved a lot. I went from a D- to a B+ in just 4 days.

[@betobtw5372]

I actually learned more from you than from my math class. Thank you so much ‼️

[@jaylenedasleeze]

wait you actually taught me more than I learned in class.

[@Mena2fly]

it took 2 days to find one problem and I came to your channel you are my savior thank you y'all need to subscribe to herrrrrrrrrrrr. I have a test tomorrow and I will ace it because of you 😍❤️

[@Ko-rf3br]

You’ve helped me more than any other teacher!

[@karinafranklin8977]

Thank you. My teacher does not know how to teach... Your videos have made my frustrations more like accomplishments

[@lyatomulyata4699]

thank you so much,i spent weeks trying to understand exponential, but after 24mins of watching your video,i understand and am ready for questions on exponentials

[@ms.smithsmathtutorials]

I am so glad it helped! Thank you for sharing this with me!

[@starkamuala]

thank you so much! this is the first time i fully understand exponetial word problems..

[@aubreymaesalazar6266]

I'm struggling with my assignment with population growth but thanks I've found this channel. it creates so much ease to learn the process and answer my assignment. you are a great tutor or teacher 'coz you take the process one at a time for it to be more understandable. I hope to learn again with the new videos. Thanks a lot.

[@ivanmendoza2044]

Thanks to you, I now understand both concepts. 😁🙏

[@RealSlopeDude]

Excellent variety of exponential word problems. I like using the equation b = 1 + r and using that as the base. I especially like how you explain the adjustment of the exponent to account for doubling every so often, for instance.

[@hatsukotaro]

this is the pinnacle of youtube. just helping people.

[@ms.smithsmathtutorials]

Thank you! I am happy the video helped!

[@OmakYaHabibi]

Top notch explanation.

[@jennmaalouf4840]

This helped my 8th grader understand the concepts!

[@briannalugo2643]

This helped soo much, thank you!

[@ashlynnmckenna2261]

Thank you so so so so so much I have been so stressed about this and this helped me so much thank you thank you.

[@KOOKIE-eh1cq]

Now!! My questions are answered thankks sm

[@marylouvelasco4750]

Thank you! Thank you! Thank you! I actually understand now.

[@mkmishra391]

Really helpful 😊

[@bhabejoyvelbestre1073]

Thank you for this video, i finally understand my lesson, just felt ggreat❤

[@bhabykongprobinsyana8205]

Thank you now I got it

[@faridajamal5824]

thank you so much for explaining each problem in detail

[@mylesken6122]

Your explanations are clear and understandable. Thank you.

[@rajcodes100]

Good job

[@keyramiller9030]

thank you thank you

[@terencevergara3087]

thank you

[@mohamedatya9490]

Amazing

[@MatthewWilde-uc7rm]

Thank you!

[@lexiesmiski]

Thank you so much for this helps a lot

[@rockstarfamily4158]

thx alot

[@microbiologist433]

i really liked that when you said oops 🙈

[@netba_art]

this was really helpful, thank you!

[@anjugani93]

thx sm

[@Isabella-jk2iq]

thank you so much! my teacher did not teach us this at all.

[@erielpena2480]

Thank you so much for this video

[@asiojanelle6856]

Thanks girl.

[@sajahamdan9287]

Studying for a test, thank you soooo, much

[@doorr1231]

good video just need tell people where you get the 1 for you 2 step value on the percentage

[@susanharris2306]

This video is awesome!

[@jordyjojo3352]

thank you sm this helped a lot!

[@ricarooooo]

This helped a lot

[@nathaniellukas8007]

i'm sorry i just don't understand how you got 14 at 18:11 Also what do you do if your base or exponent is a fraction

[@ms.smithsmathtutorials]

Thanks for asking! If the value depreciates 10% every 6 months, we want to think about how many times the car depreciates per year (annually). There are 12 months in a year and so that would mean that the car depreciates in value 2 times in 1 year (a year is made up of two 6 month periods). Given that the question is asking us about the car's value in 7 years, we have to think: how many times did the car depreciate in 7 years? For every 1 year that passes by, the car depreciates twice. So: 7 years multiplied by 2 times depreciating per year = 14 total times the car depreciated 7*2=14 If I am understanding your second question correctly, it should not make any difference if the base or exponent is a fraction. We should be able use the same formula. For example, if a problem read: "A person has $5,000 and does not add any money to it. For every year that goes by the person spends half of their money. How much money would they have after 3 months (a quarter of a year)?" The equation for this situation would be y=5,000(1/2)^(1/4) This leaves us with both a base that is a fraction and an exponent that is a fraction. When we simplify the equation, we see that this person would have $4,204.48 left after 3 months (a quarter of a year). I hope that this helps!

[@lemuelcastillano7913]

Hi! can i attach the youtube link of your video to the self-learning modules of our department in order for the students to learn more from the contents of this video aside from the modules that will be distributed to them? Thanks a lot.

[@ms.smithsmathtutorials]

Of course! Thank you!

[@bri-dn4rb]

ahhh thank you so much!! this explained everything perfectly to my friend and i :)

[@Cloud_gamesipad]

does anyone know what pen she is using?

[@ms.smithsmathtutorials]

Thanks for watching! I use Stabilo point 88 0.4 mm fineliner pens. You can sometimes find them at a local art shop or on Amazon!

[@HardikKundalwal]

Thank you😭 for boosting my confidence

[@crazypumpkin2770]

Thank you you literally saved me.

[@jjn9621]

are you wrong in the answer of the worth of the car? I got $17,069. 1-.10/2= .95 not .90. Im I correct?

[@ms.smithsmathtutorials]

Hey there! The video showing 1-.10=.90 for our b value is correct. You are correct that 1-(.10/2)=.95, but we don't need the divided by 2 part for this problem. We only need 1-.10=.90 I hope that this helps!

[@paulna5526]

I give you an A+

[@paulna5526]

I'm confused on why the formula Pe^ rt is not used????????????, can't find he plain english explanation?

[@ms.smithsmathtutorials]

Pe^rt is a compounding continuously formula while ab^x is a simple growth/decay formula. Compounding factors in interest on the principal, while ab^x does not. We use ab^x when we have a specific amount we are increasing every time (like doubling, tripling, 3%, 10%) but it is not actually compounding. In short: if the problem uses the phrase "compounding continuously" you use Pe^rt if the problem uses just "compounding" you use the compound interest formula *my video on this: kzbin.info/www/bejne/jZWUgnivpdmHrbM if the problem does not use use the word compounding at all and is just simple growth/decay, you use ab^x

[@kurtsopa]

@@ms.smithsmathtutorials There's some ambiguity in your answer concerning discrete vs continuous growth functions. In your first two examples, natural populations typically grow continuously. They do not synchronize their growth to set periods like compound interest does. Therefore, N*e^rt is the more accurate growth function. The rest of your examples are good for the ab^x function because growth occurs in discrete periods.

[@arpitkesharwani6851]

I don't understand why you have to do the 2 steps for the percents.

[@ms.smithsmathtutorials]

When the question throws a percent increase/decrease into the problem, we can't just put the percent value into the equation because we would get super inflated values that are inaccurate. 2% isn't really 2, it is technically 2/100 or .02 To break this down further, the formula is really y=a(1+r)^x for growth and y=a(1-r)^x for decay with "r" being the "rate" at which we are increasing or decreasing. When we add or subtract from the 1 for "step 2," we are finding the difference - or sum - between 1 (which would represent no change) and that rate of increase/decrease. For example, let's say you are earning 2% yearly interest (not compounded) in an online savings account and you have $100 in the account and you wanted to know how much money you have after 5 years if you don't touch it. If we did not do the "2 step" of turning the percent into a decimal and we didn't add the "1" to it for increasing we would have the incorrect formula of y=100(2)^5 which would lead us to think we will have $3,200 in your account after 5 years. This sounds wonderful! BUT unfortunately it is an incorrect amount because we did not do the 2 step. In reality, our equation would need to be y=100(1.02)^5 which leaves you with only $110.41 after 5 years. Your 2% is really a rate of .02 and you are finding the sum between 1 (no change) and the rate of .02 to determine the appropriate "b" value. I hope that helps!

[@jakirausry4805]

Thank youuu!

[@stalinmatos3296]

What kind of calculator is that

[@ms.smithsmathtutorials]

I use a Texas Instruments TI-84 Plus Silver Edition! There are many nicer and newer versions as well

[@cartervarela8497]

thank you so much i was so lost before this