10 Matching Annotations
  1. Oct 2020
  2. tienchih.github.io tienchih.github.io
    Advanced Derivatve Techniques
    1
    1. A1coffey 16 Oct 2020
      Assume that the total number (in millions) of bacteria present in a culture at a certain time ttt (in hours) is given by N(t)=3t(t−8)2+30.N(t)=3t(t−8)2+30.\begin{equation*} N(t)=3t(t-8)^2+30. \end{equation*} Find N′(t).N′(t).N'(t)\text{.} How fast is the population of bacteria growing in 10 hours?

      I could not help but think about the scientists working on a cure for Covid-19 (or any cure for any disease) after reading this. This must be extremely useful in the fight against disease to know how long bacteria takes to grow in a person blood cell. By figuring this out, scientist will be able to prescribe or manufacture new medicines based upon the results.

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    tienchih.github.io/Sec_AdvancedDerivative.html
  3. tienchih.github.io tienchih.github.io
    Derivative of Logarithms
    1
    1. A1coffey 16 Oct 2020
      Suppose the demand function for q units of a certain item is p=D(q)=150+40ln(q),q>1,p=D(q)=150+40ln⁡(q),q>1,\begin{equation*} p=D(q)=150+\frac{40}{\ln(q)}, q>1, \end{equation*} where ppp is in dollars. Find the marginal revenue. Approximate the revenue from one more unit when 6 units are sold.

      This is a great example of what companies face everyday with. Just the other day at work, we were trying to figure out what the demand would be on a new item that we are going to be selling next month. The closer we are to the actual demand the better off we will be because we could either have too much inventory or not enough.

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    tienchih.github.io/DerivativeLogs.html
  4. tienchih.github.io tienchih.github.io
    Derivative of Exponentials
    1
    1. A1coffey 16 Oct 2020
      The quantity of a drug injected in a patient is D(t)=te−0.25tD(t)=te−0.25t\begin{equation*} D(t)=te^{-0.25t} \end{equation*} where DDD is measured in mL and ttt is in minutes after injection.

      I like how the text uses real life examples. This is a good example of everyday life. If you take aspirin for a headache, you like to know how fast it will start working and for how long. I just simplified the example as doctors and nurses use this every time they administer medicine to a patient.

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    tienchih.github.io/DerivativeExp.html
  5. tienchih.github.io tienchih.github.io
    Basic rules of the derivative
    1
    1. A1coffey 14 Oct 2020
      Insulin affects the glucose, or blood sugar, level of some diabetics according to the function G(x)=−0.2x2+450,G(x)=−0.2x2+450,

      After reading this section, it really stuck with me. My grandmother had diabetes and had to take insulin. In my previous job as a firefighter, there were many times when I got called to a medical emergency and had to help the patient administer insulin. This example not only reminds me of insulin but all medicines that doctors, nurses, medical personnel give there patients and need to know how the patient is taking to it.

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    tienchih.github.io/Sec_RulesofDerivative.html
  6. tienchih.github.io tienchih.github.io
    The Derivative Function
    1
    1. A1coffey 14 Oct 2020
      Recall that in Example 7.2.2, we found the average rate of change in the height, f(x)=−5x2+20x,f(x)=−5x2+20x,f(x)=-5x^2+20x\text{,} of a rocket xxx seconds after launch , over the intervals [0,2],[0,1],[0,0.5].[0,2],[0,1],[0,0.5].[0,2], [0,1], [0,0.5]\text{.} But what prompted this discussion was what the speed was at the moment of launch. We can't actually evaluate the average rate of change over [0,0],[0,0],[0,0]\text{,} but what we can do is find the average rate of change over [0,h][0,h][0, h] and see what happens as h→0.h→0.h\to 0\text{.}

      After reading this section, I wonder how Elon Musk and Jeff Bezos with their private space companies must use this when they are testing a new rocket. It must be fascinating to listen to their scientists use the math to figure out how fast the rocket is going, the distance it will travel, the time it takes to get to space, etc.

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    tienchih.github.io/Sec_DefofDerivative.html
  7. tienchih.github.io tienchih.github.io
    Limits & Continuity
    1
    1. A1coffey 01 Oct 2020

      Please tell me if I am understanding this reading correctly. In order for the graph to be continuous it cannot have any breaks in it or "jumps." Am I correct to assume that?

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    tienchih.github.io/Sec_LimitsContinuity.html
  8. Sep 2020
  9. tienchih.github.io tienchih.github.io
    Compound Interest
    1
    1. A1coffey 23 Sep 2020

      This topic helps in so many ways. Whether you use a credit card or paying the mortgage, you will see compound interest in most daily stuff. The better you understand this topic, the better off you are in life. After buying my first property I was not familiar with this topic but after 3 houses, I totally understand it better.

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    tienchih.github.io/Sec_CompoundInterest.html
  10. tienchih.github.io tienchih.github.io
    Simple Interest
    1
    1. A1coffey 23 Sep 2020

      After reading this weeks topic on simple interest, the sticking point for me is this comes in handy when looking at all the different banks you could deposit your money. Actually taking the time to figure interest rates out will help you choose the best account to get the most out of the rates.

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    tienchih.github.io/Sec_SimpleInterest.html
  11. matthematics.com matthematics.com
    Modeling Revenue, Costs, and Profit
    1
    1. A1coffey 16 Sep 2020

      When reading this weeks assignment, a real sticking point was the break even point. This is big for companies. Companies would like to know at what point they will break even (the sooner the better) and after that start making a profit. As the text said, banks will want to know this before it lends any money because they will get paid back.

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    URL

    matthematics.com/redoak/images/maybart-2-2.pdf
  12. tienchih.github.io tienchih.github.io
    Introduction to Functions
    1
    1. A1coffey 09 Sep 2020

      A "sticking point" for me would be the vertical line test. In order to know if a relation is a function then it must pass at most one time on the curve.

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    tienchih.github.io/Sec_Functions.html