Question 1179585
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The value,$V, of a house n years after it was built is given by the formula V = 250000e^an. When n = 3, V = 350 000. 
(a) Find the initial value of this house. 
(b) Find the value of a. 
(c) Estimate the number of years for this house to double in value.
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<pre>
(a)  The initial value of this house is  250,000  (it is the value provided by the formula at n = 0).

     It is the <U>ANSWER</U> for the part (a).



(b)  Find the value of "a" from this equation  (the value in 3 years)

         350000 = {{{250000*e^(a*3)}}}


     Divide both sides by 25000

         {{{350000/250000)}}} = {{{e^(3a)}}}

         1.4 = {{{e^(3a)}}}


     Take natural logarith (base e) of both sides

         ln(1.4) = 3a*ln(e) = 3a

         a = {{{ln(1.4)/3}}} = 0.112157.   


      It is the <U>ANSWER</U>  for the part (b).


         +--------------------------------------------------------------+
         |   I made this solution and these computations to show you    |
         |   HOW SIMPLE they are.                                       |
         |                                                              |
         |   You do not need make the tons of unnecessary calculations  | 
         |   that @MathLover1 does.                                     |
         +--------------------------------------------------------------+



(c)  When they ask you to estimate the number of years for this house to double its value,

     then FOR SURE whey consider the doubling of the INITIAL value, if the opposite is not stated explicitly.


     So, your equation to find "n" is THIS

         500000 = {{{250000*e^(0.112157*n)}}}.


     Notice that I used the value of "a"  0.112157, which I found in part (b).


     In the equation, divide both sides by 250000 to get

         {{{500000/250000}}} = {{{e^(0.112157*n)}}}

               2 = {{{e^(0.112157*n)}}}


     Take natural logarith base e of both sides

              ln(2) = 0.112157*n

     and find "n"

               n = {{{ln(2)/0.112157}}} = 6.18 years.


     It is the <U>ANSWER</U> to part (c).
</pre>

Solved.


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From my post, &nbsp;learn how to solve the problem in the shortest way, &nbsp;without making unnecessary calculations.


Also, &nbsp;note that the answer by &nbsp;@MathLover1 &nbsp;to part &nbsp;(c) is &nbsp;IRRELEVANT.