The point $P(16 , 6 )$ lies on the curve $y = \sqrt{ x } + 2$. Let $Q$ be the point $(x, \sqrt{ x }+ 2 )$.

a.) Find the slope of the secant line $PQ$ for the following values of $x$. (Answers here should be correct to at least 6 places after the decimal point.)

If $x= 16.1$, the slope of $PQ$ is:
If $x= 16.01$, the slope of $PQ$ is:
If $x= 15.9$, the slope of $PQ$ is:
If $x= 15.99$, the slope of $PQ$ is:

b.) Based on the above results, estimate the slope of the tangent line to the curve at $P(16 , 6 )$.