using Matlab

Consider the model for lead transport in the body that was discussed briefly in a lecture several weeks ago. The mathematical model is given by the following system of ODEs. Xi (koi + k21 + k31)x + k2x2 + k3x3 + gi(t) x2' = k21x1 (ko2 + k2)x2 xz' = k31x] k13x3 " Note: xi is the concentration of lead in the blood X2 is the concentration of lead in soft tissues xz is the concentration of lead in the bones A particular controlled study of lead intake and excretion by healthy volunteers led to the following estimated values for the first-order rate coefficients kij in the equations. koi = 0.0211; = k12 = 0.0124; ki3 = 0.000035; ko2 = 0.0162; k21 = 0.0111; k31 = 0.0039. = The units of all these rate coefficients is (day). Hence, the independent variable (time) in these equations is assumed to be measured in units of days. The dependent variables Xi, i = 1,2,3, have units of micrograms (of lead). Task #3. Repeat Task #2 assuming that the lead intake is reduced by a factor of one- half at the after 200 days, and then continued at this constant level thereafter. Plot on a single graph the amount of lead in the blood, in the bones, and in the tissues as a function of time covering a period of 1000 days. Consider the model for lead transport in the body that was discussed briefly in a lecture several weeks ago. The mathematical model is given by the following system of ODEs. Xi (koi + k21 + k31)x + k2x2 + k3x3 + gi(t) x2' = k21x1 (ko2 + k2)x2 xz' = k31x] k13x3 " Note: xi is the concentration of lead in the blood X2 is the concentration of lead in soft tissues xz is the concentration of lead in the bones A particular controlled study of lead intake and excretion by healthy volunteers led to the following estimated values for the first-order rate coefficients kij in the equations. koi = 0.0211; = k12 = 0.0124; ki3 = 0.000035; ko2 = 0.0162; k21 = 0.0111; k31 = 0.0039. = The units of all these rate coefficients is (day). Hence, the independent variable (time) in these equations is assumed to be measured in units of days. The dependent variables Xi, i = 1,2,3, have units of micrograms (of lead). Task #3. Repeat Task #2 assuming that the lead intake is reduced by a factor of one- half at the after 200 days, and then continued at this constant level thereafter. Plot on a single graph the amount of lead in the blood, in the bones, and in the tissues as a function of time covering a period of 1000 days