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

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.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.