How can i find b?

Question

A 43 mg of a vaccine is given to a patient to prevent measles. The vaccine leaves the body at a rate of
5.2% per hour.

b-The number of milligrams of vaccine in the body after h days is how many times as large as the number of milligrams of vaccine initially injected into the body?

Answer 1

This question is a common exponential growth/decay problem.

 

Since the rate is decreasing, the amount can be modeled as   A  = A₀(e-^0.052*t)  where t is given in hours.

h days => 24h hours.

 

So the amount of h days    A = A₀(e-^0.052*24h) =  A₀*(e^-1.248h)

 

The question ask for the ratio of A to A0  which is  A₀(e^-1.248h)/A₀ = e^-1.248h