The drug concentration in the bloodstream after injection is given approximately by C(t) = 4.35e^-t. What is the rate of change after 3 hours and after 5 hours?

Answer 1

Since the question is asking for the rate of change, you want to take the derivative of C(t). By the chain rule, the derivative of C(t), dc/dt, is equal to -4.35e^-t

Therefore the rate of change after 3 hours and 5 hours can be calculated by plugging in 3 and 5 for t

C'(3) = -4.35e^-3

C'(5) = -4.35e^-5

Answer 2

Since the question asks for the rate of change, you want to first take the derivative of C(t). By chain rule, dC/dt = -4.35e^-t. You can now plug in t=3 and t=5 to find the rate of change after 3 hours and 5 hours.

C'(3)= -4.35e^-3

C'(5)= -4.35e^-5

Answer 3

dC/dt = -4.35e^-t

Now just plug in t=3 and t=5 for your answer.