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. 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, …

10. 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

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

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