Let Q(t) = the mass (mg) remaining after t hours.
We are told that Q diminishes by 3% every hour.
When t = 0, Q = 4 mg
When t = 1, Q = 4*0.97 mg
When t = 2, Q = 4*(0.97)² mg
By induction,
Q'(t) = 0.97Q
Therefore the rate of decrease is 3% per hour.
The person receives an additional dosage when Q falls to 0.50 mg. This happens when
After the second injection, the mass is now 4.5 mg. Therefore
When the mass again reaches 0.50 mg, then
Answers:
(a)
(b) 3% per hour
(c) 68.3 hours
(d) 72.1 hours
We are told that Q diminishes by 3% every hour.
When t = 0, Q = 4 mg
When t = 1, Q = 4*0.97 mg
When t = 2, Q = 4*(0.97)² mg
By induction,
Q'(t) = 0.97Q
Therefore the rate of decrease is 3% per hour.
The person receives an additional dosage when Q falls to 0.50 mg. This happens when
After the second injection, the mass is now 4.5 mg. Therefore
When the mass again reaches 0.50 mg, then
Answers:
(a)
(b) 3% per hour
(c) 68.3 hours
(d) 72.1 hours