グローバルビジネスで役立つ数学(37)指数の法則(英語版)

Hi there!

In my EIKEN® Grade 1 class, I always give a vocabulary question about the word “exponential.” Then how is it used in collocations? It is not too much to say this word is a prerequisite for the exam.

“Exponential growth” is a classic or typical example: “Exponential growth in the automobile industry is a thing of the past.” As a matter of fact, its collocation often comes out in my Business English Class as well. To be honest, I’m sick, tired, and disgusted by materialism, and I would say, “No more automobiles and smartphones, please!”

Exponential growth is nothing but the inception of either volatility or portends a return to a stagnant business. Every cloud has a silver lining; however, one time, you jump on the bandwagon in the exponential growth, then in no time are thrown into the abyss of despair.

It is no exaggeration to say that exponential growth is the writing on the wall. For your reference, “the writing on the wall” is used to say that it looks pretty likely that something will not exist much longer or someone will fail.

Today, I will boil down the laws of exponents in their word problem.

Find the value of the following exponents.
\(\displaystyle\left\{(\frac{9}{25})^{\frac{4}{3}}\right\}^{-\frac{3}{8}}\)

Here is my solution to the problem.

\(\displaystyle\left\{(\frac{9}{25})^{\frac{4}{3}}\right\}^{-\frac{3}{8}}\)
\(= (\frac{9}{25})^{-\frac{1}{2}}\)
\(= \displaystyle\left\{(\frac{3}{5})^{2}\right\}^{-\frac{1}{2}}\)
\(= \frac{5}{3}\)

I am not yet an excellent exponent to elaborate on how vital in mathematics an exponent is. I will be worth being called so when I become a mathematics expert.

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

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【グローバルビジネスで役立つ数学】でもっと学習する b^^)
【参考図書】『もう一度高校数学』(著者:高橋一雄氏)株式会社日本実業出版社
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