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3.1 exponential sequences
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.
