A child is 20 inches long at birth. If we consider that the baby will grow at a rate proportional to its body size until adulthood, then the percentage of her aduit height attained can be modeled by the following logarithmic function. \[ f(x)=20+47 \log (x+2) \] where $x$ represents her age in years and $f(x)$ represents the percentage of her adult height reached at age $x$. At what age will the child reach $95 \%$ of her adult height? Round your answer to the nearest whole year, if necessary.

Step 1 ：Given the function \(f(x)=20+47 \log (x+2)\), where \(x\) represents the child's age in years and \(f(x)\) represents the percentage of her adult height reached at age \(x\). We need to find the age at which the child will reach 95% of her adult height. This means we need to solve the equation \(f(x) = 95\) for \(x\).

Step 2 ：Subtract 20 from both sides of the equation to get \(47 \log (x+2) = 75\).

Step 3 ：Divide both sides of the equation by 47 to get \(\log (x+2) = \frac{75}{47}\).

Step 4 ：Apply the inverse of the logarithm function, the exponential function, to both sides to get \(x+2 = e^{\frac{75}{47}}\).

Step 5 ：Subtract 2 from both sides to solve for \(x\), which gives us \(x = e^{\frac{75}{47}} - 2\).

Step 6 ：Using Python to simplify the final answer, we get \(x = 3\).

Step 7 ：Final Answer: The child will reach 95% of her adult height at \(\boxed{3}\) years old.