# Exponents Formula

## Exponents Formula

Exponents Formula and formulas in mathematics aid in the calculation of huge numbers and are used in a variety of real-world scenarios. For example, we can use the Exponents Formula to compute a city’s population growth, the rate of change of bacteria in a culture, the half-life of radioactive isotopes, and so on. As the name implies, an Exponents Formula is a function that involves exponents. Exponents Formula and exponential decay are the two types of Exponents Formula. In this post, we will look at the concept of an exponential function, its graph, types, and Exponents Formula, as well as some solved cases.

As the name implies, an Exponents Formula is a function that involves exponents. A mathematical function is written as f(x) = axe, where “a” is a constant greater than zero and “x” is a variable. When x > 1, the function f(x) expands as x grows larger. The base of an Exponents Formula is typically a transcendental number indicated by e. The value of “e” is roughly 2.71828. The value of x influences an Exponents Formula curve. The domain of an exponential function is a set of all real numbers R, whereas the range is a set of all positive real numbers.

## What Are the Exponents Formulas?

To answer problems involving exponents, the characteristics of exponents or rules of exponents are used. These properties are also known as major exponents rules, which must be obeyed when solving exponents. Exponents Formula features are discussed more below.

The Product Law states that am × an = am+n

Quotient Law: am/an = am-n

a0 = 1 according to the Law of Zero Exponent

The Law of Negative Exponents states that a-m = 1/am

Power of a Power Law: (am)n = amn

Law of Product Power:  (ab)m = ambm

Power of a Quotient Law: (a/b)m = am/bm

## Exponents Formulas

A negative exponent indicates how many times the reciprocal of the base must be multiplied. For instance, if a-n is supplied, it can be expanded as 1/an. That is, we must multiply the reciprocal of a, i.e. 1/a ‘n’ times. When writing fractions using exponents, negative exponents are utilised. Like –

• 2 × 3-9 = 2 × (1/39) = 2 / 39
• 7-3 = 1/73
• 67-5 = 1/675

### Examples Using Exponents Formulas

Scientific notation is the usual way of writing extremely big or extremely small numbers. Numbers are written using decimals and powers of ten in this. When a number between 0 and 10 is multiplied by a power of 10, it is considered to be written in scientific notation. When a number is larger than one, the power of ten is a positive exponent; when a number is less than one, the power of ten is negative. Let’s go over how to write integers in scientific notation with Exponents Formula:

Step 1: Add a decimal point after the first digit from the left. If a number has only one digit (excluding zeros), no decimal is required.

Step 2: Multiply that amount by a power of ten so that the power equals the number of times the decimal point is shifted.

## 1. The first prize in a radio station sweepstakes is a \$100 gift card. Every day, a name is called. If the person does not contact the company within 15 minutes, the prize will be enhanced by 2.5 per cent the next day. If there are no winners after t days, develop an equation to reflect the gift card's monetary value.

The equation for exponential growth is y = a(1 + r) ^ t.

We have, a = 100, r = 2.5% or 0.025

In the equation y = 100(1.025) ^ t, y is the amount of the gift card and t is the number of days since the contest began.

## 2. A gym sold 550 subscriptions in 2010. Since then, subscriptions have increased by 3% per year. Write an equation to represent the number of memberships sold over t years.

The equation for exponential growth is y = a(1 + r)t.

We have, a = 550, r = 3% or 0.03

In the equation y = 550(1.03)t, y is the number of subscriptions sold and t is the number of years.