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Math·Advanced Math·Nonlinear functions

hard

$f(x)=15(b{)}^x$

In the given function, $b$ is a positive constant. For every increase in the value of $x$ by $1$, the value of $f(x)$ increases by $c\%$, where $0<c<100$. Which expression gives $c$ in terms of $b$?

A

$1+\frac{b}{100}$

B

$b+100$

C

$100(b+1)$

D

$100(b-1)$