Pharmacologists model the concentration (in mg/L) of a certain medication in the bloodstream by the family of functions
y=Ce−0.4t+5,t≥0,
where t is measured in hours and C is an arbitrary real constant.
a. Part 1: Determine a differential equation of the least possible order satisfied by every member of the family. Present your answer in differential form with numerical coefficients.
b. Part 2: Given that the concentration is 13mg/L at t=0, find the particular solution for y(t).
c. Part 3: Using the particular solution from part (b), compute the first time t (in hours) at which the concentration reaches 8mg/L. Round your answer to three decimal places.