In the year 1985, a house was valued at $\$ 118,000$. By the year 2005 , the value had appreciated exponentially to $\$ 155,000$. What was the annual growth rate between 1985 and 2005? (Round your answer to two decimal places.) Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010? (Round your answer to the nearest dollar:)

Step 1 ：Given that the value of the house in 1985 was $118,000 and in 2005 it was $155,000, we can use the formula for exponential growth to find the annual growth rate. The formula is \(V = P * e^{rt}\), where \(V\) is the final value, \(P\) is the initial value, \(r\) is the rate of growth, and \(t\) is the time.

Step 2 ：Substituting the given values into the formula, we get \(155000 = 118000 * e^{20r}\). Solving this equation for \(r\), we find that \(r\) is approximately 0.013637024622679095.

Step 3 ：The annual growth rate is therefore approximately \(1.36\%\).

Step 4 ：We can then use this growth rate to find the value of the house in 2010. Substituting the values into the formula, we get \(V_{2010} = 118000 * e^{25*0.013637024622679095}\), which gives us a value of approximately $165937.3388077908.

Step 5 ：Therefore, the value of the house in the year 2010 was approximately \(\boxed{\$165,937}\).