Question 369422
{{{A=A[0]*(1.0177)^(13*t)}}}
You don't say what unit of time is used for "t". This makes it difficult to answer the question.<br>
Assuming that t is measured in years...
First we can use a rule for exponents, {{{a^(p*q) = (a^p)^q}}}, to rewrite your equation:
{{{A=A[0]*(1.0177^13)^t)}}}
Next, we can raise 1.0177 to the thirteenth power (with a calculator):
{{{A=A[0]*(1.2561950239084477)^t)}}}
With the equation in this form, and assuming that "t" is in years, we can "read" the annual growth factor: 1.2561950239084477 (or {{{1.0177^13}}}).
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[0]*(1.0177)^(((13*t))(365/365))}}}
Multiplying we get:
{{{A=A[0]*(1.0177)^((4745*t/365))}}}
which can be rewritten as:
{{{A=A[0]*(1.0177)^(4745*(t/365))}}}
Using the rule for exponents as we did before:
{{{A=A[0]*(1.0177^4745)^(t/365))}}}
This makes the annual growth rate {{{1.0177^4745}}}<br>
etc. for other measures of "t"