Exponential Growth

Exponential growth is a concept in mathematics and science that represents a rapid increase in quantity over time. It occurs when the growth rate of a quantity is proportional to its current value. This leads to a rapid acceleration in growth, with the quantity increasing at an increasing rate.

Formula for Exponential Growth

The general formula for exponential growth is given by:

Y = a * (1 + r)^t

• Y = the final amount
• a = the initial amount
• r = the growth rate
• t = time

Example

For example, if you have $1000 invested in an account with a 5% annual interest rate compounded annually, the amount of money in the account after t years can be calculated using the formula:

Y = 1000 * (1 + 0.05)^t

Study Guide

To understand exponential growth, it's important to remember the following key points:

1. Exponential growth occurs when the growth rate of a quantity is proportional to its current value.
2. The general formula for exponential growth is Y = a * (1 + r)^t, where Y is the final amount, a is the initial amount, r is the growth rate, and t is time.
3. When solving problems involving exponential growth, make sure to use the correct units for time and the growth rate.
4. Exponential growth is commonly observed in population growth, investment growth, and the spread of diseases.

By understanding these key points and practicing problems involving exponential growth, you can gain a better grasp of this important mathematical concept.