1. Objectives:
1. Define and apply natural base
exponential functions.

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. 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. 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. If $1000 is invested at 8% annual
interest, how much will you have
after one year if interest is
compounded:
Quarterly?
Daily?

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. 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. After one year during which
interest is compounded quarterly,
an investment of $800 is worth
$851. What is the effective
annual yield?

9. What is the effective annual
yield if you invest $200 and it is
worth $297 after 1 year?

10. Any quantity, such as population,
where compounding happens “all
the time” can be expressed:

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?