SOLUTION: A=A0(1.0177)^13*t what is the annual growth factor?

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Question 369422: A=A0(1.0177)^13*t what is the annual growth factor?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A=A%5B0%5D%2A%281.0177%29%5E%2813%2At%29
You don't say what unit of time is used for "t". This makes it difficult to answer the question.

Assuming that t is measured in years...
First we can use a rule for exponents, a%5E%28p%2Aq%29+=+%28a%5Ep%29%5Eq, to rewrite your equation:
A=A%5B0%5D%2A%281.0177%5E13%29%5Et%29
Next, we can raise 1.0177 to the thirteenth power (with a calculator):
A=A%5B0%5D%2A%281.2561950239084477%29%5Et%29
With the equation in this form, and assuming that "t" is in years, we can "read" the annual growth factor: 1.2561950239084477 (or 1.0177%5E13).
Assuming that t is measured in days...
If t is measured in days, then the number of years in "t" days would be t/365. This means we want to see t/365 in the exponent. It takes a little creative Algebra to rewrite your equation with t/365 in the exponent. First we multiply the exponent by 365/365. This is just a one and multiplying by 1 does not change whatever you are multiplying it by:
A=A%5B0%5D%2A%281.0177%29%5E%28%28%2813%2At%29%29%28365%2F365%29%29
Multiplying we get:
A=A%5B0%5D%2A%281.0177%29%5E%28%284745%2At%2F365%29%29
which can be rewritten as:
A=A%5B0%5D%2A%281.0177%29%5E%284745%2A%28t%2F365%29%29
Using the rule for exponents as we did before:
A=A%5B0%5D%2A%281.0177%5E4745%29%5E%28t%2F365%29%29
This makes the annual growth rate 1.0177%5E4745

etc. for other measures of "t"