Apply $(ab)^r=a^r b^r$ and $(a^m)^n=a^{mn}$ to simplify $96^{\frac{x+1}{5}}$.

Try rewriting $2^{x+1}$ as $2^{10}\cdot 2^{x-9}$ and $3^{\frac{x+1}{5}}$ as $3^2\cdot 3^{\frac{x-9}{5}}$ so the coefficient becomes $f(9)$.

In Desmos, enter F‌rom a​nі​kо‍.‍ai

$y=(5/12)\cdot 96^{(x+1)/5}$

(use parentheses around $(x+1)/5$).

Add a table for the expression and enter $x=9$. The corresponding $y$-value is $k$.

Enter each answer choice as another function (for example, $y_1=3840\cdot 2^{x-9}\cdot 3^{(x-9)/5}$). The correct choice will match the original graph exactly and will show $k$ as the coefficient.

Factor $96$ as $3\cdot 2^5$ and apply exponent rules:

So

Substitute $x=9$:

Rewrite each factor so the part corresponding to $x=9$ is separated: ani⁠кo.аі

Substitute these into $f(x)$ and combine constants:

Therefore, the correct choice is $f(x)=3840\cdot 2^{x-9}\cdot 3^{\frac{x-9}{5}}$.