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.)

Step 1 ：We are given that in the year 1985, a house was valued at $118,000. By the year 2005, the value had appreciated exponentially to $155,000. We are asked to find the annual growth rate between 1985 and 2005.

Step 2 ：The value of the house appreciated exponentially, which means it followed the formula: \(V = P * e^{rt}\), where \(V\) is the final value of the house, \(P\) is the initial value of the house, \(r\) is the annual growth rate (which we are trying to find), \(t\) is the time in years, and \(e\) is the base of the natural logarithm (approximately equal to 2.71828).

Step 3 ：We can rearrange this formula to solve for \(r\): \(r = \frac{ln(V/P)}{t}\)

Step 4 ：We know that \(V = \$155,000\), \(P = \$118,000\), and \(t = 2005 - 1985 = 20\) years. We can plug these values into the formula to find \(r\).

Step 5 ：Substituting the given values into the formula, we get \(r = \frac{ln(155000/118000)}{20}\)

Step 6 ：Solving the above expression, we get \(r = 0.013637024622679095\)

Step 7 ：Converting this to a percentage, we get \(r = 1.36\%\)

Step 8 ：Final Answer: The annual growth rate between 1985 and 2005 was approximately \(\boxed{1.36\%}\)