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angelZ3947
24.03.2020 •
Mathematics
The quantity of a drug Q mg present in the body t hours after an injection of the drug is given is : Q = f (t) = 70 te-0.6tFind f (1), f ' (1), f (6), and f ' (6). give units and interpret the answer.Round your answer to two decimal placesf(1) = f '(1)= f(6)= f '(6)= Interpretation of f (1) and f ' (1):One hour after the drug was administered, the quantity of drug in the body is approximately Interpretation of f (6) and f ' (6) :Six hours after the drug was administered, the quantity of drug in the body is approximately
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Ответ:
A) f(1) =38.43mg
B) f'(1) = -15.37 mg/hour
C) f(6) = 11.47mg
D) f'(6) = -4.97mg/hour
F) 23.06mg
H) 0
Step-by-step explanation:
Given the function:
Q = 70te^-0.6t(1)
Where Q is measured in mg and t is in hours
(A) f(1) is the quantity Q in mg after 1 hour
f(1) = 70(1)e^-0.6(1) = 70e^-0.6
= 70×0.5488
= 38.43 mg
(B) f'(1) = dQ/dt, at t=1
= 70t × -0.6e^-0.6t +70e^-0.6t
= -42te^-0.6t + 70e^-0.6t
= -42(1) × 0.5488 + 70 × 0.5488
=28 × 0.5488
= -15.37mg/hour
(C) f(6) = 70te^-0.6t
= 70(6)e^-0.6(6)
= 420e^-3.6
= 420 × 0.0273
= 11.47mg
(D) f'(6) = dQ/dt, at t= 6
f' = -42te^-0.6t + 70e^-0.6t
f'(6) = -42(6)e^-3.6 + 70e^-3.6
= -252 × 0.0273 + 70 × 0.0273
= -6.8796 + 1.911
= -4.9686
= -4.97mg/hour
(E) f(1) is the quantity of the drug present in the body 1 hour after injection.
f'(1) is the rate of decrease of the drug 1 hour after injection or it is the rate at which the drug is decreasing 1 hour after injection.
(F) The quantity Q is given by
Q= 38.43 - 15.37
= 23.06mg
(G) f(6) is the quantity of the drug present in the body 6 hours after injection
f'(6) is the rate at which the drug is removed or decreased from the body 6 hours after injection.
(H) The quantity is given by
Q = 11.47 - 4.97×6
Q= 11.47-29.82
Q= -18.35mg
This is not possible, hence after 6 hours of injection the quantity of drug remaining is zero.
Ответ:
This factorization is not a prime factorization. 22, 54, 8 and 112 are even numbers, so they are not prime (there is only one number that is even and prime - 2).
Correct prime factorization:
so: