The equation $N(m) = 63(Q)^{\frac{m}{6}}$ gives the predicted populat…

Question

Prompt

The equation

N (m) = 63 (Q)^{\frac{m}{6}}

gives the predicted population

N (m)

, 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

180

seconds. What is the value of

p

in terms of

Q

100 (Q^{30} - 1)

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

100 (Q^{30} + 1)

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