A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for the value of the home. The model will have the form

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.

step-by-step explanation: you take each of the numbers and divide by the amount then you take the range

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