Exponential Growth and Decay Concepts

This video tutorial covers the modeling of exponential growth and decay, explaining how to use exponential functions to represent the increase or decrease of a quantity over time. It includes instructions on using graphing calculators to visualize these functions, discusses the end behavior, domain, and range of exponential functions, and provides examples of both growth and decay scenarios. The tutorial concludes with a review of key concepts and answers to common questions.

What is the primary difference between exponential growth and decay?

• Growth involves addition, decay involves subtraction.

• Growth is linear, decay is quadratic.

• Growth and decay are both constant.

• Growth decreases over time, decay increases.

In an exponential growth function, what happens to the graph as x increases?

• The graph decreases.

• The graph increases towards infinity.

• The graph remains constant.

• The graph approaches zero.

What is the domain of an exponential growth function?

• x is between 0 and 1

• x is between -1 and 1

• x is between negative infinity and positive infinity

• x is between 0 and infinity

What is the y-intercept of the function f(x) = 200 * 1.1^x?

• 200

• 0

• 300

• 100

In an exponential decay function, what happens to the graph as x decreases?

• The graph decreases towards negative infinity.

• The graph approaches zero.

• The graph increases towards infinity.

• The graph remains constant.

What is the asymptote of an exponential decay function?

• x = 1

• x = 0

• y = 0

• y = 1

How do you model an exponential growth function?

• y = a * t^b

• y = a * (1 + r)^t

• y = a * (1 - r)^t

• y = a * b^t

If a town's population decreases by 3% annually, what is the decay factor?

• 0.03

• 1.03

• 1.00

• 0.97

What equation should be used to model a decrease in quantity over time?

• y = a * (1 + r)^t

• y = a * t^b

• y = a * (1 - r)^t

• y = a * b^t where b > 1

What is the key characteristic of an exponential function with a base greater than 1?

• It oscillates.

• It represents growth.

• It remains constant.

• It represents decay.