e: The coolest number you’ve never heard of.

Hello, curious teenagers! Get ready to embark on an exciting journey into the world of mathematics with Euler’s number, also known as ‘e’. You may be wondering, what’s the big deal about this number? Well, prepare to be amazed because ‘e’ is like a celebrity mathematician who turns up in the most unexpected places, from finance to biology and beyond.

Let’s turn back the clock and travel back in time to the 18th century, when a brilliant mathematician named Leonhard Euler discovered this extraordinary number. Euler stumbled upon ‘e’ while researching the growth of compound interest. Imagine you have some money invested, and the more frequently the interest is compounded, the more your money grows, well ‘e’ is the magic number that appears when you continually increase interest, like an endless dance of numbers.

‘e’ is the base of natural logarithms, and it’s like a secret ingredient that makes exponential functions great. These functions describe all kinds of natural phenomena, from population growth to the decay of radioactive elements. Think of ‘e’ as the engine that drives change and growth, helping us understand how things evolve over time.

Imagine that you deposit $1,000 in a bank that accrues interest annually at a rate of 100%. Your money would double every year. But what if the bank capitalizes interest more frequently? What happens if it is capitalized twice a year? Or four times? As compounding intervals increase, you’ll witness an amazing phenomenon: your investment approaches a magic number called ‘e’ multiplied by its initial amount. It’s like the secret party trick of compound interest!

You may be wondering, “So what is the exact value of ‘e’?” Set for endless decimal expansion: 2.71828182845904523536… and it goes on forever without repeating. Like pi, ‘e’ is an irrational number that refuses to be expressed as a simple fraction. It’s like a mysterious puzzle that keeps mathematicians on their toes, challenging them to discover its secrets and patterns. So next time you come across ‘e’ in your math class or encounter it in the real world, give it a nod of appreciation. Remember, ‘e’ holds the key to unlocking the mysteries of growth, change and natural phenomena. Keep exploring, and who knows? You might discover your own mathematical wonders along the way!