  Let $(A,\mathfrak{m})$ be a regular local ring of dimension $d \geq 1$, $I$
an $\mathfrak{m}$-primary ideal. Let $N$ be a non-zero finitely generated
$A$-module. Consider the functions \[ t^I(N, n) = \sum_{i = 0}^{
d}\ell(\text{Tor}^A_i(N, A/I^n)) \ \text{and}\ e^I(N, n) = \sum_{i = 0}^{
d}\ell(\text{Ext}_A^i(N, A/I^n)) \] of polynomial type and let their degrees be
$t^I(N) $ and $e^I(N)$. We prove that $t^I(N) = e^I(N) = \max\{ \dim N, d -1
\}$.
