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Math·Advanced Math·Nonlinear functions

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The equation $N(m)=65(Q{)}^{\frac{m}{4}}$ gives the predicted population in thousands, of a certain bacteria colony $m$ minutes after the initial measurement, where $Q$ is a constant greater than $1$. The predicted population increases by $p\%$ every $120$ seconds.

What is the value of $p$ in terms of $Q$?

A

$100\left(Q^{\frac{1}{2}}+1\right)$

B

$100\left(Q^{30}+1\right)$

C

$100\left(Q^{\frac{1}{2}}-1\right)$

D

$100\left(Q^{30}-1\right)$