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Given:
The value of home in 2011 is $95,000.
The value of home in 2018 is $105,000.
To find:
The exponential model for the value of the home.
Solution:
The general exponential model is
...(i)
where, a is initial value and b is growth factor.
Let 2011 is initial year and x be the number of years after 2011.
So, initial value of home is 95,000, i.e., a=95,000.
Put a=95000 in (i).
...(ii)
The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.
Taking 7th root on both sides, we get
Put in (ii).
Therefore, the required exponential model for the value of home is , where x is the number of years after 2011.