There are various exponent laws in mathematics. Exponent rules are used to solve many mathematical problems that involve repeated multiplication processes. The laws of exponents simplify multiplication and division operations and make it easier to solve problems. In this article, we will go over the six most important exponent laws, along with numerous solved examples.
Introduction to Exponential Functions
The exponential function is a type of mathematical function that can be used to determine the growth or decay of a population, money, or price that grows or decays exponentially.
Jonathan was reading a news article about the most recent bacterial growth research. He discovered that an experiment was carried out with a single bacterium. After an hour, the bacterium had doubled in size and was two in number. The number was four after the second hour. Every hour, the number of bacteria increased. He was wondering how many bacteria would be left after 100 hours if this pattern continued. When he asked his teacher about it, he was given the concept of an exponential function as an answer.
When the value of a quantity increases in exponential growth and decreases in an exponential decay, the exponential function appears.
Why Do We Use Exponential Functions?
- Exponential functions are used to model populations, carbon date artifacts, assist coroners in determining the time of death, compute investments, and for a variety of other purposes. Population growth, exponential decay, and compound interest are three of the most common applications.
- Exponential functions are used in a variety of applications, including compound interest, sound volume, population growth, and population decline, as well as radioactive decay. In these problems, we’ll use the methods of building a table and identifying a pattern to help us devise a solution strategy.
What are Exponents?
Exponents are important because it is difficult to write products where a number is repeated by itself many times without them. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5 × 5 × 5.
There is no distinction between exponents and powers. So exponents are also known as powers, and adding an exponent to something is the same as elevating it to the level of a power. Exponents are simply a shortcut for indicating repeated multiplication of the same thing.
When you see an exponential function, you’ll notice the larger number at the bottom, followed by a small number in the upper right-hand corner. The large number at the bottom is known as the “base,” and the small number in the corner is known as the exponent. You’re always adding the exponent to the base.
Importance of Exponents
Exponents are useful in math because they allow us to shorten something that would otherwise be extremely long to write. If we wanted to express the product of x multiplied by itself 7 times in mathematics, we’d only be able to write it as xxxxxxx, x multiplied by itself 7 times in a row if we didn’t use exponents. So we need a different way to express that value, which is where exponents come in. Rather than writing out x multiplied by itself seven times, we can write x^7.
Basic Rules of Exponents
The exponent rules are the 0 rule, the 1 rule, the exponent power rule, the negative exponent rule, the product rule, and the quotient rule. They are the rules you use to simplify exponent problems and solve exponent problems. And, when simplifying exponent problems, you should apply the rules in the order I just listed, because exponents have their own set of operations.
When the exponent is zero, you apply the 0 rule. According to the rule, anything raised to the power of 0 equals one. The only exception is 0 (0, an indeterminate form).
To understand the concept of exponents and exponential functions in an easy and fun manner you can visit the Cuemath website.