The time required for workers to produce each unit of a product decreases as the workers become more familiar with the production procedure. It is determined that the function for the learning process is $T^{\prime}(x)=2+0.3\left(\frac{1}{x}\right)$, where $T(x)$ is the time, in hours, required to produce the xth unit. Find the time required for a new worker to produce units 10 through 16 . A. $30.83 \mathrm{hr}$ B. $-3.86 \mathrm{hr}$ C. $12.14 \mathrm{hr}$ D. $32.83 \mathrm{hr}$

Step 1 ：The problem is asking for the total time required to produce units 10 through 16. This can be found by integrating the function \(T'(x) = 2 + 0.3/x\) from 10 to 16. The integral of a function gives the area under the curve, which in this case represents the total time spent.

Step 2 ：The result of the integration is a mathematical expression \(T = -0.3\log(10) + 0.3\log(16) + 12.0\). To get the numerical value, we need to evaluate this expression.

Step 3 ：After evaluating the expression, we get \(T_{value} = 12.1410010887737\).

Step 4 ：Final Answer: The time required for a new worker to produce units 10 through 16 is approximately \(\boxed{12.14 \mathrm{hr}}\).