MATH APPLICATION IN REAL LIFE?

Blog Entry #6 by STEM D-iary

Students nowadays question their teachers, professors and even their parents about the application of their lessons especially in Mathematics.

We all know the application of basic mathematics, add, subtract, divide and multiply. But when you reach the age where you encounter broaden mathematics, you're going to ask this questions to yourselves.

Photo Courtesy: authorSTREAM

 What about Logarithms

Well maybe, if you're now a High School student, you may have heard the word Logarithms from your Math Teacher. If you're a Senior High School student or College student, I'm sure you know how to solve some problems involving Logarithms. Have you ever wandered where is it used in real life?

There are several ways in applying Logarithms in real life. As we go to College, we'll appreciate its help in building our country.

Today, not only in the Philippines, but in the whole world, we know that Earthquake precautions, measurements and other practices is a must priority in every country. Especially now in the Philippines, study shows that faults in the Philippines hasn't moved for years. 

According to Encyclopedia Britannica, Moment Magnitude is a quantitative measure of an earthquake's magnitude. To measure it, Japanese seismologist Hiroo Kanamori and American seismologist Thomas C. Hanks developed it in the 1970s. 

Calculations of an earthquake's size using the moment magnitude scale are tied to an earthquake's seismic moment rather than to the amplitudes of seismic waves recorded by seismographs. 

And to speak of Moment Magnitude Scale Logarithms is applied in calculating the earthquake's magnitude by it. How do I say so? Take a look on the formula used in Moment Magnitude Scale.

This formula was reported by Thatcher and Hanks (1973)

In combining the works of seismologists...

Hanks & Kanamori (1979) defined a new magnitude scale based on estimates of seismic content.

But wait... This was not taught to me when I was studying in Grade School nor Junior High School. Yes! What I learned about is the Richter Magnitude Scale and of course I am very aware that you may know this already.

Hey folks, he is Charles Richter. He developed past studies until he formulated the Richter Magnitude Scale that is taught maybe not only in the Philippines but the whole world rather. Of course, I won't include this if it doesn't involve Logarithms in it. 

The Richter Magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs. The formula is:

Now, you can conclude whether this Math lessons are applicable in real life. Or is this still insufficient? 

Let me give you other ways in applying Logarithms in real life. 

- In chemistry, logarithm is used in determining the pH and pOH values. 

- In physics, logarithm is used in measuring the sound intensity or the loudness or softness.

- In astronomy, logarithm simplified the task of many astronomers and others who spent much of their time doing tedious numerical computations.

There are a lot of ways in applying not only Logarithm, but other Mathematical equations in real LIFE!

So wake up from that questioning of yours just like us. Due to the hardness, I can understand that you will eventually question yourself or ask questions from others when to use or where to use this kind of stuffs.

This will be our last blog entry and I hope you had a blast reading it.

We thank you for your time spending reading this. For upcoming blogs, just stay tuned. '

AGAIN, THANK YOU!

From STEM D-iary Authors

Susmita Angelique Ramos

Mark Ryan Mora and

Nestor Paul Casipit

Price Gone So Down! (Blog #2 Price Decrease of Mobile Phones)

Samsung Galaxy S4

  

      According to Aaditaya, Galaxy S phones are flagship phones.A Flagship product refers to the absolute best manufacturer can give with the available technology at that time. Samsung cannot just make only one of them and let go. If they make a Galaxy S5, they cannot price it too high for S4 to retain its price. If they do so, they would be risking competition and user base.

As a result, S4 gets dropped to around ₹ 32,000 while
S5 was priced at around ₹45,000 on 2015

Now the depreciation affects S4. Though the official price is ₹ 32,000, the phone would be selling at around ₹ 25,000 to ₹ 28,000. Then comes Galaxy s6 and the same thing happens with it.

Since the technology is updating, the prices for new technology will drop. The price of older technology will drop even further.

Why does the price of mobile phone decrease?

          Mostly the market works on supply and demand principle. When the phones are launched the demands are high and supplies are less than demand so the prices are more.
When the phones are launched the companies spend huge amount in marketing.
When the time goes companies dont need that much of marketing for prevoius models thus reducing marketing cost and thus reducing price later in time.

As the time goes the demand goes down so to make the profit from previous models company decrease the price. Moreover, as company keeps launching new models in the same price segment. The companies reduce the price to kill the competion from their own previous models. 

~ https://www.quora.com/Why-do-phone-prices-decrease-after-a-certain-duration-after-launch

Predictions on Mobile Phones for the Next Upcoming Years

   

     As of today, mobile phones are considered as a necessities for this generation. Almost all  of the population are using mobile phones in their daily lives. Remarkably, phones of today are increasing in supply but the demands are decreasing. Phone manufacturers launch new mobile phones every year. 

      According to the research findings of Statista, the average selling price of smartphones worldwide from 2010 to 2019. In 2014, smartphones were sold at an average price of 291.1 U.S. dollars worldwide. In addition, The global average selling price of smartphones reached the highest figure to date in 2011, when these devices were sold for an average of 348.6 U.S. dollars. Since then, the average selling price of smartphones has constantly declined, going from 332.5 U.S. dollars in 2012 to 276.2 U.S. dollars in 2015. By 2019, this figure is forecast to drop to 214.7 U.S. dollars.

     Based on the findings,  in my own perspectives, after 10 years and so, the prices of mobile phone will soon severely decrease since new advance technology are discovered and tested. Soon enough, phones that are out of date as of today, will soon be sold in much lower price from its original price. Most old model phones will be just in stocks ready to be given as donation or as give aways. If the price of Samsung Galaxy S4 decrease from 32, 000 rupee to 28, 000 rupee after 2 years (2013 -2015), then after 10 years(2025), the price will soon drop to 12,000 rupee to 8,000 rupee. 

Decay of a Substance Model (Blog #4 Decay of a Substance)

      We can not avoid death because life has a limit. We are only living temporarly in God's Wonderland. Decomposition is a process of which a human, animal or any living things decay one's flesh after death. Even in this situation, we can apply a specific function to examine and can model a real life phenomenon. 

      Exponential decay model is used if a quantity is falling rapidly toward zero, without ever reaching zero. We should use the formula,

$\displaystyle y={A}_{0}{e}^{kt}$ where $\displaystyle {A}_{0}$ is the starting value, and e is Euler’s constant. Now k is a negative constant that determines the rate of decay. We may use the exponential decay model when we are calculating half-life, or the time it takes for a substance to exponentially decay to half of its original quantity. We use half-life in applications involving radioactive isotopes. (any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays. ~ http//www.britannica.com/science/radioactive-isotope)

       We used the information gathered through careful observation and measurement in constructing points on a graphs for us to have a function in making a mathematical model.  Exponential decay graphs composes of distinctive shape, as you can see in figure 1. It is essential to not forget that, however each part of the graph lies on the x - axis, it does have a small distance above the x - axis.

Figure 1. A graph showing exponential decay. The equation is $\displaystyle y=3{e}^{-2x}$.

 Exponential Decay. One of the common terms associated with exponential decay, as stated above, is half-life, the length of time it takes an exponentially decaying quantity to decrease to half its original amount. 

To find the half-life of a function describing exponential decay, solve the following equation:

$\displaystyle \frac{1}{2}{A}_{0}={A}_{o}{e}^{kt}$

We find that the half-life depends only on the constant k and not on the starting quantity $\displaystyle {A}_{0}$.

The formula is derived as follows

$\{\begin{array}{cc}\frac{1}{2}{A}_0=A_o{e}^{kt}& \\ \frac{1}{2}=e^{kt}& \text{Divide by}{A}_0.\\ ln\left(\frac{1}{2}\right)=kt& \text{Take the natural log}.\\ -ln\left(2\right)=kt& \text{Apply laws of logarithms}.\\ -\frac{ln\left(2\right)}{k}=t& \text{Divide by}k.\end{array}$

Since t, the time, is positive, k must, as expected, be negative. This gives us the half-life formula

$\displaystyle t=-\frac{\mathrm{ln}\left(2\right)}{k}$

HOW TO: GIVEN THE HALF-LIFE, FIND THE DECAY RATE.