The formula A = P(1.09)^t is an example of exponential growth with base 1.09. Determine an equivalent continuous growth formula using base e.

Also, what if it asks me to use a different base? (eg. 2)

Printable View

- June 17th 2009, 09:46 PMAlphaRockHow to find the Changed Base
The formula A = P(1.09)^t is an example of exponential growth with base 1.09. Determine an equivalent continuous growth formula using base e.

Also, what if it asks me to use a different base? (eg. 2) - June 17th 2009, 10:49 PMmr fantastic
Read this: The Change-of-Base Formula

- June 18th 2009, 02:57 AMSoroban
Hello, AlphaRock!

Quote:

The formula is an example of exponential growth with base 1.09.

Determine an equivalent continuous growth formula using base .

Also, what if it asks me to use a different base?

Suppose we wish to change to base

Instead of , we want , where is a constant to be determined.

We have: .

Take logs (base ): .

. .

. . Hence: .

Therefore: .

- June 18th 2009, 03:45 AMHallsofIvy
Un, Soroban, since , that reduces to , the formula we started with.

If we want to write as an exponential with base b, we have, as Soroban said, . Now take the**natural**logarithm of both sides: and so the equation becomes and .

The advantage is that your calculator has a "ln" key but not a " " key!

In particular, if b= e, then ln(b)= 1 so and .

If b= 2, then ln(b)= ln(2)= 0.6931 so and .