What is the importance of exponential and logarithmic functions?

Question

Can you decribe the real world application of exponential and logarithmic functions? such as its use in business or engineering.

Answer 1

There are so many uses for these mathematical functions.

Bacteria growth and spread of a virus is an exponential functions. As there are more and more bacteria their rate of growth increase.

In the stock market, growth of a portfolio could be an exponential function. It isn't likely but theoretically if you invest each year and the money grows at a certain rate you can use exponential functions to estimate what you'll have at some future time.

Logarithmic functions are used in sounds. Decibels are a logarithmic scale to quantify loudness.

The Richter scale used to measure the power of earthquake is also logarithmic.

So there are many many uses for these function even in every day life not just in business or engineering.

Answer 2

Exponential and logarithmic functions have tons of applications to the real world. A few that I can name off the top of my head are:
calculating returns on monetary investments - exponential functions are used a lot in calculating interest returns

fitting data curves to predict system variables in the future - such as the population in the future

calculating half lives of chemical components - different components can be made by decaying radioactive elements over a certain period of time.

and the applications go on and on and on .......................

Answer 3

Engineers DO use these functions all the time. First logarithmic functions make multiplying large numbers easy. Exponenential functions are typical solutions to differential equations.

Digitial communications are modulated by a complex exponential function.

Answer 4

Uses of logarithms
Logarithms are useful in solving equations in which exponents are unknown. They have simple derivatives, so they are often used in the solution of integrals. The logarithm is one of three closely related functions. In the equation bn = x, b can be determined with radicals, n with logarithms, and x with exponentials. See logarithmic identities for several rules governing the logarithm functions. For a discussion of some additional aspects of logarithms see additional logarithm topics.
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Science and engineering
Various quantities in science are expressed as logarithms of other quantities; see logarithmic scale for an explanation and a more complete list.
•The negative of the base-10 logarithm is used in chemistry, where it expresses the concentration of hydronium ions (pH). The concentration of hydronium ions in neutral water is 10−7 at 25 °C, hence a pH of 7.
•The bel (symbol B) is a unit of measure which is the base-10 logarithm of ratios, such as power levels and voltage levels. It is mostly used in telecommunication, electronics, and acoustics. It is used, in part, because the ear responds logarithmically to acoustic power. The Bel is named after telecommunications pioneer Alexander Graham Bell. The decibel (dB), equal to 0.1 bel, is more commonly used. The neper is a similar unit which uses the natural logarithm of a ratio.
•The Richter scale measures earthquake intensity on a base-10 logarithmic scale.
•In spectrometry and optics, the absorbance unit used to measure optical density is equivalent to −1 B.
•In astronomy, the apparent magnitude measures the brightness of stars logarithmically, since the eye also responds logarithmically to brightness.
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Exponential functions
Sometimes (especially in the context of mathematical analysis) it is necessary to calculate arbitrary exponential functions f(x)x using only the natural exponent ex:

The antilogarithm function is another name for the inverse of the logarithmic function. It is written antilogb(n) and means the same as bn.
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Easier computations
Logarithms switch the focus from normal numbers to exponents. As long as the same base is used, this makes certain operations easier:
Operation with numbersOperation with exponentsLogarithmic identity
















These relations made such operations on two numbers much easier and the proper use of logarithms was an essential skill before multiplying calculators became available. To multiply two numbers, one simply found the logarithms of both numbers on a table of common logarithms, added them and then looked up the result in the table to find the product. To compute powers or roots of a number, the common logarithm of that number was looked up and multiplied or divided by the radix. Interpolation could be used for still higher precision. Slide rules used logarithms to perform the same operations more rapidly, but with much less precision than using tables. Other tools for performing multiplications before the invention of the calculator include Napier's bones and mechanical calculators: see history of computing hardware.
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Calculus
The derivative of the logarithm function is

where ln is the natural logarithm, i.e., with base e. For b = e, the formula simplifies to

The antiderivative of the logarithm is

See also: table of limits of logarithmic functions, list of integrals of logarithmic functions.
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Generalizations

Answer 5

engineers probably won't use these much in the real world, unless they're trying to calculate how long a building is going to be standing and safely hold X number of people. These are used more so to calculate interest in banks and general monetary gains/losses. (simple&compound interest) They are also used a lot in calculating Half-lives in radioactive chemicals and distances and growth, like our universive is growing exponentially, seeing as how the distances between bodies is getting larger.

Answer 6

We use them all the time. Every day. They're neat, they're elegant, they occur everywhere in nature, and the best thing about logs is that you never have to multiply again: it all becomes addition. It's a great tool; if you want to get into engineering you have to learn it.

Answer 7

Well, I'm an engineer and in the real world, and I gotta tell ya Heart, I don't use or remeber any of that stuff... ever.

Answer 8

Which one is made out of Popsicle sticks?

Answer 9

Yes it is.