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Exponential expressions word problems (algebraic)

Given a real-world context that involves repeated multiplication, we model it with an exponential function.

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  • duskpin ultimate style avatar for user Carolyn Taylor
    at in the video, how do you figure you can add 1 to .3?
    (3 votes)
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  • aqualine seed style avatar for user Coco
    Can someone please explain the factoring part? Why does it result in 1? Thank you!
    (4 votes)
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  • female robot grace style avatar for user rama
    he wrote 170(1+0.3) where the 1 come from?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      As stated in other responses to nearly the same question...
      If something grows by 30%, you have the original amount (100%) + the new amount (30%).
      If you change these into decimals you get: 100% = 1 and 30% = 0.3
      This is where the 1+0.3 comes from.
      Hope this helps.
      FYI... get in the habit of reading the other questions and answers. They may answer your question and/or give you new insights into the problem.
      (10 votes)
  • leafers seedling style avatar for user Hana B
    why aren't you using any of the formulas? it will make it a lot easier for us to understand.
    (2 votes)
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    • winston default style avatar for user Daniel Ye
      Hi, Hana B!
      Formulas are a handy thing to use, but Sal is trying to explan the principals behind the formula. In my opinion, knowing the mechanics is much more important than just memorizing the formula.

      Hope that helped!
      (6 votes)
  • duskpin ultimate style avatar for user stbergman
    what if the percent is 0
    (1 vote)
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  • starky tree style avatar for user LovelyLuna
    When exponential expressions were first introduced in Khan Academy, I was able to write them like this:

    170(1 + 0.3)^t

    But now I'm told to write them like this:

    170(1.3)^t

    And the former version is marked wrong. Why? Is it just to simplify the expression because I've learned the concept?

    Edit: Turns out the first version isn't marked wrong, but I'm still wondering why the second is encouraged.
    (2 votes)
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  • blobby green style avatar for user avery.guidry2020
    On the day that a certain celebrity proposes marriage, 101010 people know about it. Each day afterward, the number of people who know triples.
    Write a function that gives the total number n(t)n(t)n, left parenthesis, t, right parenthesis of people who know about the celebrity proposing ttt days after the celebrity proposes.
    (2 votes)
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  • spunky sam red style avatar for user MYSTO(AKA Ni-trip)
    what if I have a question that says "there are 50 people in a party and the number of people that know about it increases by 1.5%, how do I do that??
    like: if you multiply the percent 30% is 1.3 and 75% is 1.75
    so how can 1.5% be like the others??
    (2 votes)
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  • female robot ada style avatar for user ʕ •ᴥ•ʔ Najma A.
    I have a question:
    When can we know if our growth rate should be added by 1 or not? For example in the video, Sal added 100% to the increasing growth rate of 30%. Does this always happen in every word problem example?

    Sorry if my question is hard to understand, but I'm hoping for someone to answer my question soon. I'm open to answering anyone that needs more clarification for my question! Thx :)
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      If the problem gives you the percent increase, then you start with the original amount (100%) and add the increase (30%) = 130%

      If the problem gives you a percent decrease, then you start with the original amount (100%) and subtract the decrease (30%) = 70%

      Hope this helps.
      (2 votes)
  • leaf grey style avatar for user chenrui.zhang
    Is there any other way in which you can model a real-world context that involves repeated multiplication other than an exponential function?
    (3 votes)
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Video transcript

- [Instructor] There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P of t on the reservation t years from now. All right, let's think about this. And like always, pause this video, and see if you can work it out on your own. Well, let's think about what P of zero is. P of zero, this is going to be the initial population of deer, the population at time zero. Well, we know that, that's going to be the 170 deer that we start on the reservation. Now, let's think about what P of one is. What's going to be the population after one year? Well, it's going to be our original population, 170, but then it increases at a rate of 30% per year. So it's going to be 170 plus another 30% of 170. So I could write that as 30% times 170. Or I could write this as 170 plus 0.3 times 170. 30% as a decimal is the same thing as 30/100 or 3/10. Or I could write this as, if I factor out 170, I would get 170 times one plus 0.3, which is the same thing as 170 times 1.03. And this is a really good thing to take a hard look at 'cause you'll see it a lot when we're growing by a certain rate, when we're dealing with what turns out to be exponential functions. If we are growing, well, I almost made a mistake there, it's 1.3. So here you go, 1.3. One plus 0.3 is 1.3. So once again, take a hard look at this right over here because it's going to be something that you see a lot with exponential functions. When you grow by 30%, that means you keep your 100% that you had before, and then you add another 30%. And so you would multiply your original quantity by 130%, and 130% is the same thing as 1.3. So if you are growing by 30%, you are growing by 3/10, you would multiply your initial quantity by 1.3. So let's use that idea to keep going. So what is the population after two years? Well, you would start that second year with the population at the end of one year. So it's going to be that 170 times 1.3. And then, over that year, you're going to grow by another 30%. So if you're gonna grow by another 30%, that's equivalent to multiplying by 1.3 again. Or you could say that this is equal to 170 times 1.3 to the second power. And so I think you see where this is going. If we wanted to write a general P of t, so if we just want to write a general P of t, it's going to be whatever we started with, 170, and we're going to multiply that by 1.3 however many times, however many years have gone by. So to the t power because, for every year, we grow by 30%, which is equivalent mathematically to multiplying by 1.3. So after 100 years, it would be 170 times 1.3 to the 100th power.