Overgrown Redwood Log and Wildflowers by flickr user David Sifry

The NaturalLogarithm ...(for real this time)

Properties of exponential functions

Properties of the exponential growth function

Domain: Range: Root(s): y-intercept: Increasing or Decreasing: Concavity: Asymptote(s):

For example, let's look ata > 1

Properties of exponential functions

As an example let's look at

Properties of the exponential decay function

Domain: Range: Root(s): y-intercept: Increasing or Decreasing: Concavity: Asymptote(s):

0 < a < 1

Properties of logarithmic functions

As an example we'll look at

Properties of the logarithm function

Domain: Range: Root(s): y-intercept: Increasing or Decreasing: Concavity: Asymptote(s):

a > 1

ƒ(x) = 10x y = x

Properties of logarithmic functions

As an example we'll look at

Properties of the logarithm function

Domain: Range: Root(s): y-intercept: Increasing or Decreasing: Concavity: Asymptote(s):

0 < a < 1

ƒ(x) = 12

x

Who wants to be a millionaire?

What is compound interest?

How does this formula "work"?

How much money will you have after 5 years if you invest $300.00 at 6% interest compounded annually? monthly?

The number e ...e =

... Source: e to 1 000 000 digits

The Exponential Function

The Natural Logarithm

Who wants to be a millionaire?

It turns out that when interest is compounded continuously, we use this formula to calculate the total value of the amount, A, earned on the principal, P, after any period of time, t.

How much money will you have after 5 years if you invest $300.00 at 6% interest compounded continuously?

If you invest $300.00 at 6% interest compounded continuously how long will it take to double your money?

Solve ...