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# 3.1 exponential sequences

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### 3.1 exponential sequences

1. 1. Unit 3 – Exponential Functions 3.1 Exponential Sequences
2. 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. 3. Example 1 • 2, 8, 32, 128, … • starting value: ______ •growth/decay factor: ______ •formula for next term: next = now ______ • next term: _____
4. 4. You Try! • 6, 18, 54, 162, … • starting value: ______ •growth/decay factor: ______ •formula for next term: next = now ______ • next term: _____
5. 5. Example 2 • 4, 2, 1, ½, … • starting value: ______ •growth/decay factor: ______ •formula for next term: next = now ______ • next term: _____
6. 6. You Try! • 6, 2, 2/3, 2/9, … • starting value: ______ •growth/decay factor: ______ •formula for next term: next = now ______ • next term: _____
7. 7. Example 3 • 0.5, 1.5, 4.5, 13.5, … • starting value: ______ •growth factor: ______ •formula for next term: next = now ______ • next term: _____
8. 8. You Try! • 0.25, 1.25, 6.25, 31.25, … • starting value: ______ •growth factor: ______ •formula for next term: next = now ______ • next term: _____
9. 9. Other Sequence Names •Linear sequences ▫same # added each time ▫ Also called ARITHMETIC •Exponential sequences ▫Same # multiplied each time ▫ Also called GEOMETRIC
10. 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. 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. 12. Example 4 •Write a sequence to match: •A population of bacteria will triple every month. There are currently 450 bacteria present.
13. 13. You Try! •You currently have \$85 and you will spend half your money each week.