Question
QUESTION SIX (13 marks) a) The number of milligrams of a drug in a person's system after thours is given by the function D=20e^-0.4t i. Find the amount of the drug after 5 hours. (3mks) i. When will the amount of the drug be 0.1 milligrams? (3mks)
Solution
4.1
(201 Votos)
Guilherme
Profissional · Tutor por 6 anos
Resposta
**a) i. Amount of drug after 5 hours:**To find the amount of the drug after 5 hours, we substitute *t* = 5 into the given function:D = 20e^(-0.4t)D = 20e^(-0.4 * 5)D = 20e^(-2)Using a calculator:e^(-2) ≈ 0.1353Therefore:D ≈ 20 * 0.1353 D ≈ 2.706 milligrams**Answer:** After 5 hours, there will be approximately 2.706 milligrams of the drug in the person's system.**a) ii. Time when the amount of drug is 0.1 milligrams:**To find the time when the amount of the drug is 0.1 milligrams, we set D = 0.1 and solve for *t*:0.1 = 20e^(-0.4t)Divide both sides by 20:0.005 = e^(-0.4t)Take the natural logarithm (ln) of both sides:ln(0.005) = ln(e^(-0.4t))Using the property of logarithms that ln(e^x) = x:ln(0.005) = -0.4tSolve for t:t = ln(0.005) / -0.4Using a calculator:ln(0.005) ≈ -5.298Therefore:t ≈ -5.298 / -0.4t ≈ 13.25 hours**Answer:** The amount of the drug will be 0.1 milligrams after approximately 13.25 hours.