Question

A medicine is administered to a patient. The amount of medicine M, in milligrams, in 1 mL of the patient’s blood, t hours after the injection, is
M(t)=-1/3t^2+t where 0<t<3
a. Find the rate of change in the amount M, 2h after the injection.
b. What is the significance of the fact that your answer is negative?

Answer 1

-(1/3) t^2 + t
or
-1/(3 t^2) + t
or
1/(3t^2+t)

Answer 2

If the first then
dM/dt = -(1/3)(2t) + 1

= -2t/3 + 1
if t = 2
dM/dt = -4/3 + 3/3 = -1/3

the medicine is disappearing, presumably because it is eating bad guys.

Answer 3

a)
Dependent: amount of medicine, mg
Independent: time, hour

f(x2) ---> -1/3(2)^2+2=2/3, f(x1)---> -1/3(0)^2+0=0

slope of a secant= f(x2)-f(x1) over x2 - x1

2/3 - 0 over 2 - 0 = 1/3mg/h

b) amount of medicine in 1 mL of blood being dissipated throughout the system