What does e & o insurance cover

According to the ESRB, an E rating indicates that the game may contain minimal cartoon, fantasy or mild violence and/or infrequent use of mild language. For example:

• Tim: Do you know a good E-rated game I could get my nephew for his birthday?
• Ralf: Forget the E rating! You can't go wrong with Donkey Kong!

Ecstasy

The letter E is also used in speech and text to refer to the recreational synthetic drug ecstasy. For example:

• Vicki: Can you get me some E?
• Rennie: Of course. How much do you want?

Summary of Key Points

"Everyone" is the most common definition for E in gaming related communications on apps such as Discord, TeamSpeak and Telegram.

"Ecstasy" is another common definition for E, especially among drug users.

It’s obvious that compounding more frequently results in more money in the bank. So it is natural to ask whether compounding at every instant in time (that is, continuously) leads to an infinite amount in the bank.

To answer this question we need to evaluate

   

This quantity turns out again to be

- the same base value with the property that the gradient of the graph is unity at .

Now

can be expanded very nicely using the trusty old Binomial Theorem. We find that

   

This series is convergent, and evaluating the sum far enough to give no change in the fourth decimal place (this occurs after the seventh term is added) gives an approximation for

of 2.718.

It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients). Its properties have led to it as a "natural" choice as a logarithmic base, and indeed e is also known as the natural base or Naperian base (after John Napier).

There is the remarkable property that if the function

(known as the exponential function and also denoted as "") is differentiated with respect to , then the result is the same function . The proof of this can be seen in many textbooks on elementary calculus. It’s also true that for ,

   

In fact, it is true that given the equation:

   

then a solution for

is where is a constant.

It’s also possible to relate the general exponential function,

, to the exponential function. This is because some number can always be chosen so that . Then

   

Differentiating with respect to

gives

   

which tells us that the general exponential relation,

, that so often crops up in applications, is in fact a solution of the differential equation

   

(Actually it happens to be the only type of solution to this important equation.)

It is this equation that emerges naturally when attempting to model various processes.

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About the author

Ian Garbett lectures in applied radiation/radiological physics within the Medical Radiation Science courses at Charles Sturt University, Wagga Wagga NSWAustralia.

He graduated in 1977 with a BSc Honours in Applied Physics from the University of Lancaster, and obtained an MSc in Medical Physics from the University of Leeds in 1987.

He is interested in various theoretical aspects of radiation and radiological physics, with an interest in mathematical modelling in general.

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