Exponential Functions and Compound Interest

This video tutorial covers the basics of graphing exponential functions, including their properties, transformations, and applications in growth and decay models. It explains how to graph these functions, identify their domain and range, and understand the concept of asymptotes. The tutorial also introduces the exponential growth and decay models, as well as the compound interest formula, providing examples and practice problems to reinforce learning.

What is the base 'B' in an exponential function y = a * B^X used to determine?

• The x-intercept

• The y-intercept

• The growth or decay factor

• The slope of the line

If the base 'B' of an exponential function is between 0 and 1, what type of function is it?

• Linear function

• Quadratic function

• Exponential decay function

• Exponential growth function

In graphing y = 2 * 3^X, what is the y-intercept?

• 6

• 1

• 3

• 2

What does the 'a' value in the general form y = a * B^(X-H) + K represent?

• Horizontal shift

• Vertical stretch or compression

• Base of the exponential

• Rate of growth

How does a negative 'a' value affect the graph of an exponential function?

• It reflects the graph over the x-axis

• It stretches the graph horizontally

• It compresses the graph vertically

• It shifts the graph to the right

Which formula represents an exponential growth model?

• y = a * (1 - R)^T

• y = a * (1 + R)^T

• y = a * X^2

• y = a * B^X

In the context of exponential decay, what does the 'R' in the formula y = a * (1 - R)^T represent?

• The initial amount

• The base of the exponential

• The decay rate

• The time period

What is the principal 'P' in the compound interest formula?

• The initial amount invested

• The interest rate

• The number of compounding periods

• The total amount after interest

If interest is compounded quarterly, how many times is it compounded in a year?

• 365 times

• 2 times

• 4 times

• 12 times

In the compound interest formula, what does 'n' represent?

• The number of years

• The interest rate

• The principal amount

• The number of compounding periods per year