Math 111 - 10/31/11

5.2) Exponential Functions

any where usually

Remember:

Cont, one-to-one, Domain is all reals, Range , Asymptote at , y-intercept

Applications of exponential functions - Compound interest.

Suppose you invest $1000 at 10% interest (Compounded yearly.)

5 years:

In general (for yearly compounding)

A: Amount you have now

t: What year it is

P: Original amount

r: interest rate

What about $1000 at 10% compounded quarterly.

You actually get % interest four times a year.

In one year

so in five years

In general (for compounding n times per year)

A: Amount you have now

t: What year it is

P: Original amount

r: interest rate

So $5000 at 4% compounded monthly for 10 years would be

What about $1 at 100% for one year?

Yearly:

Quarterly:

Monthly:

Daily:

Hourly:

These numbers are approaching a "special" number

Cont:

So when we have continuously compounding interest...

We can also transform any of these graphs just like before