As part of a pollution study, a model concentration c as a function of position x has been developed,
c(x) = A(e^(-x/2a) - e^(-x/a))
where A=10-5 ppm (parts per million) and a=1 m. Plot this concentration from x=0 to x= 10 m. If a vehicle with a pollution sensor travels through this atmosphere at u=U (U=20 m/s), develop an expression for the measured concentration rate of change of c with time, and plot using given data. At what location will the sensor indicate the most rapid rate of change, and what is the value of this rate of change?