SOLUTION: 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 wo

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Question 1190924: 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.
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~ 

So, we should find "t" from this equation

    5000000 = .


Divide both sides by 1000000.  You will get

    5 = .


Take natural logarithm of both sides.

    ln(5) = 0.645*t,

      t   =  = 2.495252577.


ANSWER.  In 2.5 years, approximately.


CHECK.   The annual growth factor is   =  = 1.906, approximately.

         In 2.5 years, the growth factor is   = 5.01, which confirms the answer.

Solved.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
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.
----------------------------
5000000 = 1000000e^(0.645t)
e^(0.645t) = 5
Solve for t
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