How does the resistivity of a typical semiconductor change as its temperature is increased?

1. For semiconductors the carrier number density $n$ rises sharply with temperature. 2. This increase outweighs the decrease in collision time $\tau$. 3. Since $\rho = m/(ne^2\tau)$, a large rise in $n$ lowers $\rho$. 4. Hence resistivity decreases (C); the increasing trend (A) applies to metals instead. _Source: syllabus Physics Ch 3 "Current Electricity", p.10_