Exponential Functions and Their Properties

The video tutorial explains the concepts of exponential growth and decay. It begins with an introduction to these concepts, followed by a detailed example of exponential growth using the function y = 2^x. The tutorial then explores exponential decay with the function g(x) = (1/2)^x, highlighting the differences between growth and decay. The video concludes with a comparison of the two functions, emphasizing the properties of exponential functions and their behavior as x values change.

What is the main focus of the video tutorial?

• Exponential growth and decay

• Quadratic functions

• Linear equations

• Trigonometric identities

In the function y = 2^x, what is the value of y when x = 0?

• 4

• 2

• 1

• 0

What happens to the value of y in the function y = 2^x as x becomes more negative?

• It remains constant

• It becomes negative

• It becomes infinite

• It approaches zero

In the function g(x) = (1/2)^x, what is the value of g(x) when x = -1?

• 4

• 1/2

• 1

• 2

How does the function g(x) = (1/2)^x behave as x increases?

• It grows exponentially

• It decays exponentially

• It remains constant

• It oscillates

What is the relationship between the bases of the growth and decay functions discussed?

• Both are greater than 1

• One is greater than 1, the other is a fraction

• Both are negative

• Both are fractions

What is the base of an exponential growth function?

• Equal to 1

• Greater than 1

• Between 0 and 1

• Less than 0

What is the base of an exponential decay function?

• Between 0 and 1

• Greater than 1

• Equal to 1

• Less than 0

Which of the following statements is true about exponential functions?

• Exponential functions are always quadratic

• Exponential functions are always linear

• Exponential functions grow faster than polynomial functions

• Exponential functions grow slower than polynomial functions

What determines whether an exponential function represents growth or decay?

• The value of the base

• The coefficient of x

• The sign of the exponent

• The constant term