Evaluating the Natural Exponential Function

The video tutorial introduces the natural base e, an irrational number similar to pi, and explains its properties. It demonstrates how to evaluate e^x using calculators for various x values and graph these values using ordered pairs. The tutorial also covers creating an XY chart to visualize the exponential function and provides a graphical analysis of the function's behavior, including its asymptotic properties.

What is the approximate value of the natural base e?

• 3.14

• 4.5

• 1.62

• 2.7

How is the number e similar to pi?

• Both are irrational numbers

• Both are negative numbers

• Both are integers

• Both are rational numbers

What is the function f(x) = e^x used to represent?

• Logarithmic growth

• Quadratic growth

• Exponential growth

• Linear growth

How do you evaluate e^x for x = -1 using a calculator?

• Enter ln(1)

• Enter e^-1

• Enter e^1

• Enter ln(-1)

What is the approximate value of e^-1?

• 0.367

• 7.4

• 2.71

• 1.28

What is the ordered pair for x = 0.25 in the function f(x) = e^x?

• (0.25, 0.367)

• (0.25, 1.28)

• (0.25, 2.71)

• (0.25, 7.4)

What is the approximate value of e^0.5?

• 2.71

• 0.367

• 1.28

• 1.64

What is the ordered pair for x = 1 in the function f(x) = e^x?

• (1, 1.64)

• (1, 2.71)

• (1, 1.28)

• (1, 0.367)

What is the value of e^2 rounded to the nearest tenth?

• 2.7

• 7.4

• 1.6

• 0.4

What is the value of e^0?

• 1

• 0

• 7.4

• 2.7