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Now that we know how to solve exponential equations, let's go back to money and populations and solve some harder problems.

How long will it take $3000 to grow to $8500 if it is invested in an account that earns 8% compounded quarterly?

       Set it up:

initial amount = 3000

final amount = 8500

split factor = 1.02

( remember that, each quarter, $1.00 splits into $1.02! )

       We are looking for time...

       We'll need to get the number of splits, #, then adjust it to years.

8500 = 3000 * 1.02^( # ) ... clear the path ... ( 8500 / 3000 ) = 1.02^( # ) ... ( 17 / 6 ) = 1.02^( # ) ... Use Ln to get the # down! ... Ln( 17 / 6 ) = Ln( 1.02^( # ) ) ... Ln( 17 / 6 ) = # * Ln( 1.02 ) ... Ln( 17 / 6 ) / Ln( 1.02 ) = # ... grab a calculator ... # = approximately 52.59 quarters

That's about 13.15 years.  (I divided by 4!)