Question

The drug concentration curve is given by equation: ????(????) = 5???? ∙ ????−0.4????.

Here concentration ????(????) is measured in mg/ml and time is measured in hours

a. What is the rate of drug concentration increase at t = 0?

(a) 1 mg/(ml∙hour) (b) 6 mg/(ml∙hour) (c) 2 mg/(ml∙hour)

(d) 7 mg/(ml∙hour) (e) 11 mg/(ml∙hour) (f) 3 mg/(ml∙hour)

(g) 15 mg/(ml∙hour) (h) 9 mg/(ml∙hour) (i) 10 mg/(ml∙hour)

(j) 5 mg/(ml∙hour)

b. For how may hours will the drug concentration be increasing? (Hint: the drug

concentration function increases until it reaches its maximal value, and then it starts to

decrease.)

(a) 2.5 hours (b) 1 hour (c) 10 hours (d) 4.5 hours

(e) 5 hours (f) 1.5 hours (g) 2 hours (h) 7.5 hours

(i) 3 hours (j) 3.5 hours

Answer 1

The drug concentration curve is given by the equation: C(t) = 5t^(-0.4).

a. To find the rate of drug concentration increase at t = 0, we need to take the derivative of the concentration function with respect to time:

dC/dt = -2t^(-1.4)

Substituting t = 0, we get:

dC/dt = 0

Therefore, the rate of drug concentration increase at t = 0 is 0 mg/(ml∙hour).

b. The drug concentration will be increasing as long as the derivative of the concentration function is positive. This occurs until the concentration function reaches its maximum value, which occurs when the derivative of the concentration function is 0.

To find the maximum value of the concentration function, we need to find its critical points:

dC/dt = -2t^(-1.4) = 0

Solving for t, we get:

t = 0

This is the only critical point of the concentration function, so it must be the maximum value. Therefore, the drug concentration will be increasing for 0 hours.

After t = 0, the drug concentration function will start to decrease.