  We study multivariate approximation defined over tensor product Hilbert
spaces. The domain space is a weighted tensor product Hilbert space with
exponential weights which depend on two sequences
$\boldsymbol{a}=\{a_j\}_{j\in\mathbb{N}}$ and
$\boldsymbol{b}=\{b_j\}_{j\in\mathbb{N}}$ of positive numbers, and on a bounded
sequence of positive integers $\boldsymbol{m}=\{m_j\}_{j\in\mathbb{N}}$. The
sequence $\boldsymbol{a}$ is non-decreasing and the sequence $\boldsymbol{b}$
is bounded from below by a positive number. We find necessary and sufficient
conditions on $\boldsymbol{a},\boldsymbol{b}$ and $\boldsymbol{m}$ to achieve
the standard and new notions of tractability in the worst case setting.
