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Math·Advanced Math·Nonlinear functions

hard

$$f(x)=k(1.83{)}^x$$

The function $f$ is defined by the given equation, where $k$ is a constant. The value of $f(x)$ increases by $p\%$ for every increase of $x$ by $1$. For which of the following functions, where $k$ is a constant, does the value of $g(x)$ increase by $p\%$ for every increase of $x$ by $\frac{1}{4}$?

A

$g(x)=k(1.83{)}^{\frac{x}{4}}$

B

$g(x)=k(1.83{)}^{4x}$

C

$g(x)=k(1.83{)}^{x+\frac{1}{4}}$

D

$g(x)=k(1.83{)}^{x-\frac{1}{4}}$