document.write( "Question 369422: A=A0(1.0177)^13*t what is the annual growth factor? \n" ); document.write( "
Algebra.Com's Answer #263763 by jsmallt9(3758)\"\" \"About 
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\"A=A%5B0%5D%2A%281.0177%29%5E%2813%2At%29\"
\n" ); document.write( "You don't say what unit of time is used for \"t\". This makes it difficult to answer the question.

\n" ); document.write( "Assuming that t is measured in years...
\n" ); document.write( "First we can use a rule for exponents, \"a%5E%28p%2Aq%29+=+%28a%5Ep%29%5Eq\", to rewrite your equation:
\n" ); document.write( "\"A=A%5B0%5D%2A%281.0177%5E13%29%5Et%29\"
\n" ); document.write( "Next, we can raise 1.0177 to the thirteenth power (with a calculator):
\n" ); document.write( "\"A=A%5B0%5D%2A%281.2561950239084477%29%5Et%29\"
\n" ); document.write( "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\").
\n" ); document.write( "Assuming that t is measured in days...
\n" ); document.write( "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:
\n" ); document.write( "\"A=A%5B0%5D%2A%281.0177%29%5E%28%28%2813%2At%29%29%28365%2F365%29%29\"
\n" ); document.write( "Multiplying we get:
\n" ); document.write( "\"A=A%5B0%5D%2A%281.0177%29%5E%28%284745%2At%2F365%29%29\"
\n" ); document.write( "which can be rewritten as:
\n" ); document.write( "\"A=A%5B0%5D%2A%281.0177%29%5E%284745%2A%28t%2F365%29%29\"
\n" ); document.write( "Using the rule for exponents as we did before:
\n" ); document.write( "\"A=A%5B0%5D%2A%281.0177%5E4745%29%5E%28t%2F365%29%29\"
\n" ); document.write( "This makes the annual growth rate \"1.0177%5E4745\"

\n" ); document.write( "etc. for other measures of \"t\"
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