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Math·Advanced Math·Nonlinear functions

hard

x	g(x)
4	500
5	3000
6	15500
7	78000

For the exponential function $g$, the table shows four values of $x$ and their corresponding values of $g(x)$. The function can be written as $g(x)=a^x+b$, where $a$ and $b$ are constants. If $g(m)=0$ and $g(0)=n$, where $m$ and $n$ are constants, what is the product of $m$ and $n$?

A

$-121$

B

$-124$

C

$-372$

D

$-375$