Please answer + code on Matlab... The file is written below

"hw6_data"

%The first column is time in days and the second one is measured virus concentration

data=[-10 131334 -9 130748 -8 130223 -7 132089 -6 134453 -5 133575 -4 132779 -3 132123 -2 131524 -1 130300 0 133230 1 133089 2 98668 3 73080 4 53579 5 39405 6 28333 7 19182 8 14888 9 12405 10 8043 11 6249 12 4939 13 2440 14 2003];

1. (computing) A simple model of HIV dynamics is dtdV=PcV, where P is virus production rate, V is virus concentration (per mL ), and c is the clearance rate. Suppose a protease inhibitor drug is given, resulting in production becoming 0 . (a) The text file ("hw6_data") on the website records how a patient's virus concentration changes with time. Time (measured in days) is scaled so that treatment begins on day 0 . Use this data to estimate c, assuming that once treatment starts, P=0. This can be done by plotting the natural log of virus concentration vs time after time 0 , and fitting a line through the resulting scatter plot. Make a plot of this scatter plot, and a line going through the post-treatment points. Side note: Since P does not instantly go to 0 when the inhibitor is given, this is actually a lower bound of c. As we saw in class, a better estimate (found by fitting data to a more accurate model) is c=3.1 per day. (b) Suppose that before treatment the virus production was in equilibrium. What was the production rate, P ? (This requires estimating V0, the steady state virus concentration, from the data.) (c) What is the total virus production per day (pre-treatment) if the person's fluid volume is estimated to be 15103mL ? Note: Before these calculations were done, it was thought that virus production during the latent period was small. This calculation changed how people thought of HIV dynamics