Problem 78
Question
What is the natural exponential function?
Step-by-Step Solution
Verified Answer
A natural exponential function is a function of the form \(f(x) = e^x\), where the base e is a constant approximately equal to 2.71828, and x is the exponent. For example, the natural exponential function of 2 is about 7.389056.
1Step 1: Defining Natural Exponential Function
A natural exponential function is a function of the form \(f(x) = e^x\), where the base e is a constant equal to approximately 2.71828, and x is the exponent.
2Step 2: Understanding the Nature of e
The number 'e' is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828.
3Step 3: An Example of Natural Exponential Function
Let's consider an example of a natural exponential function \( e^x \). Let's compute \( e^2 \). Substituting the approximated value of e which is 2.71828, \( e^2 = 2.71828^2 = 7.389056 \). Hence, the natural exponential function of 2 equals to 7.389056.
Other exercises in this chapter
Problem 78
Solve each logarithmic equation. Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer.
View solution Problem 78
In Exercises 75–80, find the domain of each logarithmic function. $$ f(x)=\log (7-x) $$
View solution Problem 79
The exponential growth models describe the population of the indicated country, \(A,\) in millions, t years after 2006 . $$ \begin{array}{ll} {\text { Canada }}
View solution Problem 79
Use a graphing utility and the change-of-base property to graph each function. $$ y=\log _{3} x $$
View solution