Answer to Question #31138 in Algebra for madu

Question

Pesticides are used by farmers to product their crops from insects. A farmer sprayed pesticide on his tomato cultivation Assume unknown amount R(t) litres of pesticide were sprayed on the soil. Pesticides spayed on plants have a certain outflow rate in to the soil, and conversely,pesticide in the soil has a certain uptake rate into the plants.repeated applications of the pesticides are required to control the insects, which implies the pesticide levels in the plants varies with time. Quantize the pesticide spraying as follows;
x(t)=amount of pesticide in the plant,
y(t)= amount of pesticide in the soil,
R(t)=amount of pesticide applied to the plant
t=time in year
A typical model is obtained from input output frequency domain analysis
X/R= (s+3)/((s+3)(s-2)+2)
In a pristine orchard,the initial data is X(0)=0,Y(0)=0 because the plant and the soil initially harbor no pesticide.Represent the given transfer function (X/R) in the form of partial factions.