6. It is known that a factory produced 10,000 units of a product in January, 12,000 units in February, and 13,000 units in March. In the $n$-th month, the factory produces $a b^{n}+c$ ten thousand units, where $a$, $b$, and $c$ are constants, and $n=1,2, \cdots, 12$. Then, how many ten thousand units will the factory produce in April?
6.1 .35 .

From the given conditions, we know
$$
a b+c=1, a b^{2}+c=1.2, a b^{3}+c=1.3 \text {. }
$$

Then $a b(b-1)=0.2, a b^{2}(b-1)=0.1$.
Thus $b=0.5, a=-0.8, c=1.4$.
Therefore, $a b^{4}+c=1.35$.