Our calculators are made to make your life easier at any stage of life. For example, you will probably run into the “e” at some point in your education. Whether it is in economy, algebra, physics or simple math class, It is beneficial to know something about it. To help you, we wrote an essay that explains everything most straightforwardly. But if you don’t have time to read about it, then our eˣ calculator is the perfect choice for you.
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What does e mean on a calculator?
Euler’s number (e) is a mathematical constant approximated at 2,71828. It can be characterized in many ways but is best known as the base of the natural logarithm. It is called the Euler’s number after the Swiss mathematician Leonhard Euler or Napier’s constant. This constant was discovered by another Swiss mathematician Jacob Bernoulli in the 17th Century. He found it while he was studying compound interest. There are many different ways to calculate and characterize this constant, which you will read in other paragraphs of this text.
How to calculate the “e”?
Euler’s number is very similar to the number pi. Knowing these numbers can be helpful in everyday situations and your work or school. There are two ways to calculate the value of this number, and both involve infinity. We will show you both formulas and give you quick explanations of them.
e=\sum_{n=0}^{\infty}\frac{1}{n!}e=1+\frac{1}{1}+\frac{1}{1*2}+\frac{1}{1*2*3}+…In the first shown formula, we use n as infinity. Infinity can’t be calculated, but we can make calculations that slowly get higher. We can never reach infinity, but the higher we go, the closer are we to the number e.
As you can see, the second formula is a fraction that looks a bit more complicated. But by looking closer into it, you see that it is just an ongoing series of fractions. It is the same as in the first formula; the more steps we add, the closer we are to the value of e.
How to put e in a calculator?
On a basic calculator, using e can seem a little confusing. For us, the easiest way to do it is by downloading our calculators or simply using the online version “https://calconcalculator.com/”.
If you are using a graphing calculator, first you have to press the e key, then press the exponent key ^, and after that enter in the exponent. In almost every mobile calculator, the number e already comes in with the place for the exponent, so it is effortless to enter it.
Graph of e^x
This is an exponential function which means it has a horizontal asymptote. It is an elementary graph, and here is how it looks.
Table for e^x
Like all functions, this one also has a table of values. As you can see in this picture, the value of e grows as the x grows. But if x goes below zero, the value of e decreases.
| x | eˣ |
| 1 | 2,72 |
| 2 | 7,39 |
| 0 | 1 |
| -1 | 0,37 |
| -2 | 0,14 |
Examples with e calculator
As we mentioned before, this constant has its use in many areas such as finance. We don’t want to bore you with numbers, so imagine some bank pays an 80% percent interest (40% twice a year). In finance, when calculating the compound interest, we use this formula.
(1+\frac{r}{n})^{n}n this formula, the “r” represents the annual interest rate (as a decimal), and the “n” represents the number of periods in a year. It is a very simple calculation.
As we start making the “n” bigger, the result begins to have exponential growth towards e. The Compounding Formula is very similar to the e formula (as n is closer to infinity); it just has an extra r.
FAQ
The e raised to the power infinity
When you have a function in which the x tends to infinity, then y also tends to be infinite. That means that when you raise e to infinity, it equals infinity.
The e raised to power minus infinity
In some functions, x tends to minus infinity. In that case, y tends to 0. That being said, e raised to power minus infinity equals 0.
How can I calculate e?
As we already said, there are two ways to calculate it. Both methods are effortless to understand, and both were presented earlier in the text. We use a formula that uses n as infinity in the first one. The second one is also an easy fraction, but you have to know about the factorial sign. This isn’t a crucial thing to know, especially if you are using a calculator.
What is the value of e power 0?
As with every other number, when we put it to power 0, it equals 1. The same goes for thee. When putting this constant to the power 0, it comes out as 1. Things like this are common knowledge, and you don’t need a calculator for them.
What is the value of e power 1?
The same thing applies to this. When we put any number to power 1, it stays the same. This constant is no different; when putting it to power 1, its value of 2,71828 remains unchanged.
