Use mathematics to teach you the momentum of 1,000 yuan to spend 1 million yuan

Time: One day in July 1752.

Location: Fields of Philadelphia in the United States.

The sky was so gloomy, the wind whispered, the dark clouds rolled, the thunder sounded in the air, and the lightning was like the sharp sword that split through the sky. The rain began to fall, and people ran into the house to avoid. In chaos, a middle -aged man brought a young man, under the wind and rain, and struggled to the wilderness. Middle -aged people have a big kite, which is a special kite:

The noodles of the silk are bound to a wire on it, and the fine hemp rope of the kite is tied to this iron wire, and a copper key hangs on the lower end of the hemp rope. The kites rolled higher and higher, and the rain gradually became more and more dense. Suddenly, there was a lightning light in the air, and the man trembled for a while, and his hand felt numb. He tried to put his fingers close to the copper key again, and the blue spark flashed between his fingers and the key!

At this moment, the middle -aged people were very excited. He forgot to call: "I was shocked! I finally proved that the lightning was electric!" Later, he introduced the electricity on the kite line into the Leidon bottle.

The above is a famous experiment in the history of science. The middle -aged person who conducted this experiment was a famous scientist in the United States, an inventor of the lightning rod, and Benjaminfranklin (1706-1790). The young man who followed him was his son.

Benjamin Franklin

Franklin worked for the scientific and democratic revolution in his life. The property left after his death was not considerable, and it was roughly only 1,000 pounds. Surprisingly, he left a will that allocated millions of pounds of property! This interesting will is written like this:

"... 1,000 pounds to the residents of Boston, if they accept the 1,000 pounds, then this money should be entrusted to some selected citizens, and they have to lend the money to some young manual operators at 5%per year. Go to life. This money has increased to 131,000 pounds after 100 years. I hope that at that time, 100,000 pounds were used to build a public building, and the remaining 31,000 pounds continued to give birth to 100 years. This model increased to 4061,000 pounds, of which 1061,000 pounds were dominated by residents of Boston, and the remaining 30,000 pounds were managed by the public in Massachusetts. Since then, I dare not make more claims! "

Franklin died in 1790, and the last period of his will was around 1990. You may not help but ask: Franklin, a scientist, left 1,000 pounds, and a millionaire -like will. Could it be "fainted"? Intersection Let's calculate according to Franklin's idea.

Franklin's inheritance calculation table

The upper formula is obviously a function y = a, when A = 1.05 is special.

The function of mathematics, such as y = A, is called the index function, where A is agreed to be more than 0 and not equal to 1 constant.

The image above draws the image of three functions. It is easy to see from the image: when the bottom A is greater than 1, the index function is increasing, and the more and faster; otherwise, when the bottom A is less than 1, the index function decreases.

Let us observe the changes in the value of B = 1.05 in the reason, it is not difficult to count:

When x = 1, B = 1.05

When x = 2, B = 1.103;

When x = 3, B = 1.158;

Native

When x = 100, B = 131.501.

This means that in the above story, the property of Franklin at the end of the first 100 years should increase

This is 501 pounds more than Franklin's will! At the end of the second 100 years, he had more property:

It can be seen that Franklin's will is scientifically standing!

Meatful funds, low interest rates, under the mysterious index effect, can become dazzling. This is the revelation of Franklin's story! It is really one of them because they have not been able to realize this in history. It is one of them.

Napoleon Bonaba

Napoleon is still a person who has a fate with mathematics. So far, there is still a geometric theorem, which belongs to his name. This theorem is: if the triangles are made of all sides of any triangle, their outer rounded hearts are connected to the connected heart of the same edge, as shown in the figure.

However, the general had inadvertently trapped the vortex of the index effect!

In 1797, when Napoleon visited a national primary school in Luxembourg, he gave a bouquet of 3 gold Louis roses, and promised that as long as the French Republic exists for a day, he will send a bouquet of roses with equal values ​​a year. As a symbol of the friendship between the two countries. Since then, Napoleon has forgotten this promise due to the battle of fire and sword!

Nearly a century later in the long river of time, in 1894, the Kingdom of Luxembourg solemnly proposed a "rose suspension case" to the Republic of France, requiring the French government to choose one of the reputation of Napoleon and the debt of 1375596 francs. Essence The huge sum of money for millions of francs is the principal of 3 Golden Louis, with a 5%annual interest rate, under the product of the index effect in 1997.

However, the index effect is more positive. Many people use it effectively to make themselves the owner of knowledge and wealth!

The US Apple Computer Corporation was established by two young entrepreneurs in 1977. They worked together and worked hard to make sales increase at an average annual growth rate of 171%. In just 6 years, their sales increased from 2.5 million US dollars to nearly $ 1 billion:

Apple has also become a world -renowned large company from an inconspicuous small company crowded in the garage. Two young people have also become the master of billions of wealth!

Index functions are not only widely used in mathematics, physics, and astronomy, but also very useful in other natural sciences and even social sciences!

The natural phenomenon and social phenomenon that changes in the rules of the index has a very important feature, that is, the amount A change amount ΔA is always proportional to the amount A itself and its change time Δt

Mathematically proves that the amount in the upper right end bracket, when the change time is short, tends to a limit k (actually equal to LNA), so as to prove

Conversely, mathematicians have also proved that if the amount of measure A is proportional to its itself and the change time (the proportion coefficient is K), then there must be

Here A is the initial value of variable A (t = 0), count E = 2.718 ... is a mathematical constant as important as the pi. From the settlement of bank interest to the growth of bacteria, and even the decline of the atomic nucleus, E can be seen everywhere.

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Does not represent the position of the Institute of Physics of the Chinese Academy of Sciences

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Source: Original Reading

Edit: Paarthurnax

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