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Math·Advanced Math·Nonlinear functions

hard

The function $f$ is defined by $f(x)=a^x-b$, where $a$ and $b$ are constants. In the $xy$-plane, the graph of $y=f(x)$ passes through the points $(c,9)$ and $(2c,249)$, where $c$ is a constant. Which of the following could be the value of $b$?

A

7

B

24

C

240

D

258