Exponential Functions and Equations

This video tutorial covers the interpretation of exponential functions, including their general form and how they can represent growth or decay. It explains how to interpret graphs of exponential functions and solve related equations. The tutorial also includes a real-life example of exponential growth, demonstrating how to model situations using exponential equations.

What is the primary characteristic of an exponential function?

• It remains constant.

• It always decreases.

• It can demonstrate both growth and decay.

• It only increases.

Which of the following is the general form of an exponential function?

• f(x) = ax^2 + bx + c

• f(x) = a * b^x

• f(x) = a/b

• f(x) = a + bx

In the general form of an exponential function, what does 'a' represent when it equals 1?

• The function's exponent

• The function's y-intercept

• The function's slope

• The function's base

What does the graph of an exponential growth function typically look like?

• A straight line

• A curve that decreases

• A curve that increases rapidly

• A horizontal line

Which equation represents exponential growth?

• y = x^2

• y = 3^x

• y = 1/x

• y = 0.5^x

What happens to the y-values in an exponential decay graph as x increases?

• They oscillate.

• They decrease rapidly.

• They remain constant.

• They increase rapidly.

Which equation represents exponential decay?

• y = x^2

• y = 0.5^x

• y = 1/x

• y = 3^x

In an exponential function, what does 'B' represent when it is greater than 1?

• Constant rate

• Zero rate

• Growth rate

• Decay rate

What is the value of 'a' in the exponential function f(x) = b^x?

• x

• b

• 1

• 0

How do you determine the correct equation from a table of values?

• By checking each equation with a given x-value

• By guessing

• By using a calculator

• By looking at the graph