Science:Math Exam Resources/Courses/MATH103/April 2017/Question 05/Statement

In a petri dish with a radius of $r=3{\text{cm}}$ scientists placed a bacteria killing agent along a diameter. They found the density of bacteria, $\rho (x)$, increased with distance $x$ cm from the diameter according to $\rho (x)=kx$ ${\text{bacteria}}/{\text{cm}}^{2}$ for some constant $k$. Determine the total population size of bacteria, $N$, in the petri dish.