Understanding Exponential Growth and Decay

The video reviews exponential growth, explaining how values double as x increases, and introduces exponential decay, where values halve. It demonstrates these concepts using tables and graphs, highlighting key features like asymptotes and the behavior of exponential functions compared to linear ones. The video also discusses the mathematical representation of these functions, emphasizing the role of the common ratio and y-intercept.

What happens to the value of y when x increases by 1 in exponential growth?

• y doubles

• y halves

• y remains constant

• y triples

In the exponential growth equation y = 3 * 2^x, what does the number 3 represent?

• The common ratio

• The slope

• The x-intercept

• The y-intercept or initial value

What is the shape of the graph for exponential growth?

• A parabola

• A straight line

• A curve that rises steeply

• A hyperbola

In exponential decay, what happens to the value of y when x increases by 1?

• y remains constant

• y halves

• y doubles

• y triples

What is the common ratio in the exponential decay equation y = 3 * (1/2)^x?

• 1/2

• 2

• 1

• 3

How do the graphs of exponential growth and decay compare?

• They are identical

• They are parallel

• They are mirror images over the y-axis

• They are mirror images over the x-axis

What happens to the graph of an exponential decay function as x becomes more positive?

• It approaches zero

• It approaches infinity

• It becomes a straight line

• It oscillates

What is the condition for exponential growth in terms of the common ratio?

• The common ratio is greater than 1

• The common ratio is less than 1

• The common ratio is negative

• The common ratio is equal to 1

What happens when the common ratio r is equal to 1 in an exponential function?

• The function grows

• The function remains constant

• The function oscillates

• The function decays

In general, what does a common ratio less than 1 indicate in an exponential function?

• Stability

• Growth

• Oscillation

• Decay