Fitting Data: Bacteria

Scientists have been investigating whether a new chemical $($which due to non$-$disclosure agreements, we will call "Chemical X$")$ deters the growth of certain bacterial

colonies. They have varied the concentration of Chemical $x$ and measured how long it takes for an inital sample of $10$ cells to grow to fill the Petri dish.

The scientists are not sure from a quick look at the data whether a quadratic or cubic fit wil be better for this data, so you are to complete the MATLAB code below to

perform both data fits. Then the program will plot the data for you. The data are provided in two vectors in the code.

Script $o.$

$\%$ Input data

concentration $=[0$:$\mathrm{.}1$:$2\mathrm{.}5]$;$\%$ concentration of chemical in M$/$L

$\%$ time until Petri dish is filled

$\%$ Perform a quadratic fit of the data

$\%$ Complete the two lines below, replacing $...$ with the appropriate code for a quadratic fit

c$\_$quad $=...,\%$ find the coefficients

quad$\_$fit $=$dots calculate values for the fit

$\%$ Perform a cubic fit of the data

$\%$ Complete the two lines below, replacing $...$ with the appropriate code for a cubic fit

c$\_$cube $=$dots,$\%$ find the coefficients

cube$\_$fit $=$dots,$\%$ calculate values for the fit

$\%$ Plot both fits and the original data on the same axes

plot$($concentration$,$ time,$\text{'}*\text{'},$ concentration, quad$\_$fit, $\text{'}-\text{'},$ concentration, cube$\_$fit, $\text{'}$k$--\text{'})$;

legend$(\text{'}$Data$\text{'},$ 'Quadratic fit', 'Cubic fit'$)$;

title$(\text{'}$Effectiveness of Chemical $x$ in Preventing Bacterial Growth'$)$;

xlabel$(\text{'}$Concentraton $($M$/$L$)\text{'})$;

ylabel$(\text{'}$Time to fill dish $($days$)\text{'})$;