Modeling Exponential Growth Using Patterns

The video tutorial explains how to model geometric change using sequences. It begins with an introduction to geometric sequences and the concept of a common ratio. An example is provided to illustrate how each term in a sequence is derived by multiplying the previous term by a common ratio. The tutorial then presents a problem involving photocopy enlargement, demonstrating how to calculate the size of an image after multiple enlargements using a geometric sequence. Another problem involving a dot pattern is analyzed to determine if a specific number of dots can be achieved. The lesson concludes by summarizing the key concepts of modeling exponential growth through patterns.

What is the common ratio in a geometric sequence?

• The result of dividing one term by its preceding term

• The product of all terms

• The sum of consecutive terms

• The difference between consecutive terms

If a picture is enlarged by 150% each time, what is the common ratio used in the sequence?

• 1.0

• 0.5

• 2.0

• 1.5

How do you calculate the size of an image after multiple enlargements using a geometric sequence?

• Add the initial size to the number of enlargements

• Divide the initial size by the number of enlargements

• Multiply the initial size by the common ratio raised to the power of the number of enlargements

• Subtract the initial size from the final size

In the dot problem, what is the common ratio used to determine the number of dots in each step?

• 2

• 4

• 1

• 3

Can the sequence in the dot problem ever reach exactly 332 dots?

• No, it cannot reach exactly 332 dots

• Yes, at step 12

• Yes, at step 10

• Yes, at step 8