{{ option.icon }} {{ option.label }} arrow_right
{{ option.icon }} {{ option.label }}
{{ option.icon }} {{ option.label }}

# Exponential Function

tune
{{ topic.label }}
{{ result.displayTitle }}
{{ result.subject.displayTitle }}
navigate_next

# Exponential Function

An exponential function is a nonlinear function that can be written in the following form, where and As the independent variable changes by a constant amount, the dependent variable multiplied by a constant factor. Therefore, consecutive values form a constant ratio.

Here, the coefficient is the intercept, which is sometimes referred to as the initial value. The base can be interpreted as the constant factor. The graph of an exponential function depends on the values of and expand_more

## Why

unfold_more
If the coefficient is the function becomes a horizontal line.
This is a line along the axis and, therefore, is a linear relation. This means that if then the function is not exponential. info

Further explanation about a difficult or interesting topic.

expand_more

## Why and

unfold_more
If the base is negative, the function gives undefined results for certain values. For example, since a negative value for would yield non-real values for Hence, a condition on is needed.
However, if or , the function becomes a horizontal line.
Therefore, cannot be equal to nor info

Further explanation about a difficult or interesting topic.

Study online with Mathleaks, at the forefront of mathematics. Available on mobile and computer, all math courses are interconnected following the curriculum. Easily find content and theories for the subject you are studying. Exercises with associated answers, hints, and solutions – all connected in one place, and easy to use.

Community (beta)