Question 1190924
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A house is purchased for 1,000,000 in 2002. 
The value of the house is given by the exponential growth model A= 1,000,000e^(0.645)(t). 
Find t when the value of the house would be worth 5,000,000.
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<pre>
So, we should find "t" from this equation

    5000000 = {{{1000000*e^(0.645*t)}}}.


Divide both sides by 1000000.  You will get

    5 = {{{e^(0.645*t)}}}.


Take natural logarithm of both sides.

    ln(5) = 0.645*t,

      t   = {{{ln(5)/0.645}}} = 2.495252577.


<U>ANSWER</U>.  In 2.5 years, approximately.


<U>CHECK</U>.   The annual growth factor is  {{{e^0.645}}} = {{{2.718^0.645}}} = 1.906, approximately.

         In 2.5 years, the growth factor is  {{{1.906^2.5}}} = 5.01, which confirms the answer.
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Solved.