# Science:Math Exam Resources/Courses/MATH103/April 2006/Question 01 (d)

MATH103 April 2006

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### Question 01 (d)

The concentration of a protein in a long, thin cylindrically shaped bacterium is given by the function $\displaystyle c(x)$ where c is measured in mol/μm along the long axis of the cell and $\displaystyle 0 is measured in μm. Suppose that when the cell divides, it splits at $\displaystyle x=3/2$ μm and that all protein to the left of this point ends up in the left daughter cell and any to the right ends up in the right daughter cell. Determine which of the following statements is necessarily true:

i. If the centre of mass of the protein density is to the left of the median of the density, then the cell on the right gets more than half of the total protein.

ii. If the centre of mass of the protein density is at $\displaystyle x=1$ μm, then the cell on the left gets more than half of the total protein in the mother cell.

iii. If the median of the protein density is at $\displaystyle x=1$ μm, then the cell on the left gets more than half of the total protein in the mother cell.

iv. If the mean and median are at the same point, both cells get the same amount of protein.

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