Students will extend patterns with exponential growth and decay, make near and far predictions about the pattern, describe the pattern in words, and determine the general term.

Intentionality…

The purpose of the Day 4 activities is to reinforce key concepts from Day 3. Students will engage in a math talk, analyzing graphical representations of exponential patterns, and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas:

• Patterns can be extended because they are repetitive by nature.
• Pattern rules are generalizations about a pattern, and they can be described in words.
• One common use of patterns is predicting future events.
• A pattern can be extended to make a prediction. 
• For far predictions, calculations are required for efficiency. 
• An expression that represents repeated multiplication of the same factor is called a power.
• Exponential growth is a pattern of data that shows greater increases with passing time.
• Exponential growth is a pattern that increases at a rate proportional to its current value.
• Exponential decay is a pattern that decreases at a rate proportional to its current value.
• Exponential growth is a pattern of data that shows greater increases with passing time.
• Exponential decay occurs when the base is greater than 0 and less than 1. 
• In a power, the base number is defined as a number which is multiplied by itself. 
•  In a power, the exponent represents the number of times the base number is multiplied.
• Graphical representations of exponential growth appear as a curved line.