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)
Read this: The Change-of-Base Formula
Hello, AlphaRock!
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: .
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 .