Exploring Exponential Functions: An Introduction

This video introduces exponential functions, contrasting them with linear functions. It explains how linear functions involve constant addition, while exponential functions involve multiplication, leading to growth or decay. The video covers identifying initial values and growth or decay factors, using examples to illustrate these concepts.

What type of function is described by the equation y = mx + b?

• Quadratic function

• Logarithmic function

• Exponential function

• Linear function

In a linear function, how does the value change with each step?

• It divides by a constant.

• It adds a constant.

• It decreases by a constant.

• It multiplies by a constant.

What distinguishes an exponential function from a linear function?

• The change is always subtracting.

• The change is always adding.

• The change involves division.

• The change involves multiplication.

How does an exponential function differ from a quadratic function?

• By having a higher degree

• By having a variable in the exponent

• By having a constant slope

• By having a variable base

How can you describe the growth in an exponential function?

• By multiplying by a base number

• By subtracting a constant value

• By dividing by a base number

• By adding a constant value

What does the 'a' in the general form of an exponential function represent?

• The variable in the exponent

• The base of the exponential function

• The initial value of the function

• The rate of growth or decay

What is the role of the 'b' in the general form y = a * b^x of an exponential function?

• It signifies the y-intercept.

• It represents the slope.

• It is the growth or decay factor.

• It indicates the initial value.

What happens when the growth factor in an exponential function is greater than 1?

• The function remains constant.

• The function oscillates.

• The function grows.

• The function decays.

In the context of exponential functions, what does decay mean?

• The function's values increase over time.

• The function's values double over time.

• The function's values decrease over time.

• The function's values remain constant over time.

What is the initial value in an exponential function?

• The base of the exponential function

• The coefficient of the exponent

• The value of the function at x=0

• The rate of growth or decay