$15 \cdot 36$ For real numbers $x, y$, define the operation "*": $x * y=a x^{y}+b+1$. If $1 * 2=969, 2 * 3=983$, then $2 * 9$ equals
(A) 1988.
(B) 1989.
(C) 1990.
(D) 1991.
(Xi'an, Shaanxi Province, China Junior High School Mathematics Competition, 1990)
［Solution］ From the given, we have
$$
\left\{\begin{array}{l}
a \cdot 1^{2}+b+1=969, \\
a \cdot 2^{3}+b+1=983,
\end{array}\right.
$$

Solving, we get $\quad a=2, \quad b=966$.
$$
\therefore \quad 2 * 9=2 \cdot 2^{9}+966+1=1991 \text {. }
$$

Therefore, the answer is $(D)$.