The document discusses exponential sequences, providing examples and explanations of key terms like exponential sequence, growth/decay factor, starting value, and formula. It gives examples of sequences that exponentially grow, like 2, 8, 32, 128, and sequences that exponentially decay, like 4, 2, 1, 1/2. Readers are prompted to identify the starting value, growth/decay factor, formula, and next term for sequences. The document also distinguishes between linear and exponential sequences and asks readers to identify which type of sequence is being described.

1. Unit 3 – Exponential Functions
3.1 Exponential Sequences

2. Exponential Sequence Vocab:
• Exponential Sequence: Sequence where
terms are multiplied by some number to
find the next term
• Growth/Decay Factor: what each term is
being multiplied by
▫ > 1 for exponential growth
▫ < 1 for exponential decay
• Starting Value: the first term in the
sequence
• Formula: tells how to find the next term
▫ Example: next = now x 2

3. Example 1
• 2, 8, 32, 128, …
• starting value: ______
•growth/decay factor: ______
•formula for next term:
next = now ______
• next term: _____

4. You Try!
• 6, 18, 54, 162, …
• starting value: ______
•growth/decay factor: ______
•formula for next term:
next = now ______
• next term: _____

5. Example 2
• 4, 2, 1, ½, …
• starting value: ______
•growth/decay factor: ______
•formula for next term:
next = now ______
• next term: _____

6. You Try!
• 6, 2, 2/3, 2/9, …
• starting value: ______
•growth/decay factor: ______
•formula for next term:
next = now ______
• next term: _____

7. Example 3
• 0.5, 1.5, 4.5, 13.5, …
• starting value: ______
•growth factor: ______
•formula for next term:
next = now ______
• next term: _____

8. You Try!
• 0.25, 1.25, 6.25, 31.25, …
• starting value: ______
•growth factor: ______
•formula for next term:
next = now ______
• next term: _____

9. Other Sequence Names
•Linear sequences
▫same # added each time
▫ Also called ARITHMETIC
•Exponential sequences
▫Same # multiplied each time
▫ Also called GEOMETRIC

10. Identifying Exponential Sequences
•Tell if each sequence is linear,
exponential, or neither:
• 4, 24, 144, 864, …
• 9, 16, 25, 36, …
• 5, 4.5, 4, 3.5, …
•

11. Writing Sequences
•From a given verbal description:
•Find the starting value – this is the
first term
• Find the growth/decay factor –
multiply the first term by that #
•Keep multiplying until you have 4
terms

12. Example 4
•Write a sequence to match:
•A population of bacteria will triple
every month. There are currently 450
bacteria present.

13. You Try!
•You currently have $85 and you
will spend half your money each
week.