Question

A 0.4 ml dose of a drug is injected into a patient steadily for half a second. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.5% per second. Using formulas, express Q as a continuous function of time, t in seconds.

Q=___________ for 0 ≤ t ≤ 0.5

and

Q=___________ for 0.5 < t

Thanks :)

Answer 1

for the first one, Q=___________ for 0 ≤ t ≤ 0.5, i'm not sure... would it be either

(4/5) t ?

or 0.4t ? :/

and i'm kinda lost on the second one.

Q=___________ for 0.5 < t

i'm thinking that it starts off with 0.4e^ of something.. :/ but I'm not even sure if thats right haha :/

Answer 2

The initial amount is 0.4,
the 0.5% per second means that after each second, 99.5% remains. Convert that to a decimal an...

Q = 0.4(0.995)^t

Answer 3

for this Q=___________ for 0 ≤ t ≤ 0.5

it's injected steadily, ie linearly. 0.4 mL for 0.5 seconds... means 0.4/0.5 mL/second, or 4/5*t

Answer 4

ohh okay :)

so this equation, Q = 0.4(0.995)^t, is for 0.5 < t ?

Answer 5

ohh that's what i mixed up haha

so the first one is (0.4/0.5)t ?

Answer 6

0.4/0.5 = 4/5

Answer 7

okay awesome!! thanks :)

Answer 8

okay awesome!! thanks :)