Question

A 507 mm³ of a vaccine is given to a patient to prevent the flu. The vaccine leaves the body at a rate of 0.7% per hour.

a. Define a function V that gives the mass of the vaccine remaining in the body in terms of the number of hours, t since the vaccine was dministered.

b. How much of the vaccine remains in the body 24 hours after it was administered?

c. How much of the vaccine remains in the body 1 week after it was administered?

Answer 1

To define a function V that gives the mass of the vaccine remaining in the body, subtract the rate of decrease per hour multiplied by the number of hours from the initial mass of the vaccine given to the patient.

Step-by-step explanation:

To define a function V that gives the mass of the vaccine remaining in the body, we need to consider the rate at which the vaccine leaves the body.

The rate at which the vaccine leaves the body is given as 0.7% per hour.

Let's assume the initial mass of the vaccine given to the patient is 507 mm³. We can use the formula:
V(t) = Initial mass - (Rate of decrease per hour x t)

Using this formula, we can calculate the remaining mass of the vaccine after any given number of hours.

For part b, we substitute t = 24 hours into the function V(t) to find how much of the vaccine remains in the body after 24 hours.

For part c, we substitute t = 1 week (which is 7 days or 168 hours) into the function to find how much of the vaccine remains in the body after 1 week.