Modeling Exponential Decay: Using Tables and Function Notation

The video tutorial explains how to model exponential decay using tables and function notation. It begins with a comparison of linear and exponential functions, using a linear function example to illustrate the concept. The tutorial then introduces exponential decay through a paper-tearing activity, demonstrating how the area decreases by half with each tear. The exponential decay function is explained, highlighting the difference in graph appearance compared to linear functions. Function notation is used to model exponential decay, with examples provided to show how to calculate values using the formula y = a * b^x.

What is the initial value in the linear function example provided?

• 0

• 64

• 32

• 1/2

In the paper-tearing example, what is the area of the paper after three tears?

• 2 units

• 16 units

• 4 units

• 8 units

What is the decay factor in the exponential decay function example with the paper?

• 4

• 2

• 1/2

• 1/4

In the function notation y = a * b^x, what does 'b' represent?

• Exponent

• Base

• Initial value

• Decay factor

If the initial value is 10 and the decay factor is 1/4, what is the function notation?

• y = 1/4 * 10^x

• y = 10 * 1/4^x

• y = 1/2 * 10^x

• y = 10 * 1/2^x