Upcoming SlideShare
×

# 5 4 the number e

546 views

Published on

Published in: Education, Technology
1 Like
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
546
On SlideShare
0
From Embeds
0
Number of Embeds
77
Actions
Shares
0
5
0
Likes
1
Embeds 0
No embeds

No notes for slide

### 5 4 the number e

1. 1. Objectives: 1. Define and apply natural base exponential functions.
2. 2. Discovered by mathematician Leonhard Euler. (Sounds like “oiler”) Called the natural base e or the Euler number. Very common in higher math, especially calculus.
3. 3. The irrational number e is defined: Means as n increases, gets closer and closer to e ≈ 2.718 n 10 100 1000 10,000 100,000 1,000,000
4. 4. Compound interest can be measured using the equation: where P is principal, and n is the number of times interest is compounded per year.
5. 5. If \$1000 is invested at 8% annual interest, how much will you have after one year if interest is compounded: Quarterly? Daily?
6. 6. As n gets very large the interest formula approaches . Example: How much will you have from the last example if interest is compounded continuously?
7. 7. Compound/continuous interest yields annual growth that is greater than the annual interest rate indicates. The actual growth is described by the Effective Annual Yield. To find: Divide then write increase as a %.
8. 8. After one year during which interest is compounded quarterly, an investment of \$800 is worth \$851. What is the effective annual yield?
9. 9. What is the effective annual yield if you invest \$200 and it is worth \$297 after 1 year?
10. 10. Any quantity, such as population, where compounding happens “all the time” can be expressed:
11. 11. A population of ladybugs multiplies rapidly so the population after t days is How many ladybugs are present now? How many will there be after a week?