Question

A 0.6 ml dose of a drug is injected into a patient steadily for one 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 0.2% per second. Express Q as a continuous function of time t in seconds. Use the form given below.

Q(t)= { A(t), 0 ≤ t<1
{ B(t), 1 13 years ago

Answer 1

Any ideas on how to start?

Answer 2

I honestly have no idea..

Answer 3

"increases steadily"

Answer 4

linear for the first part..

Answer 5

starts at 0 mL at t=0 ends at .6 mL at t=1 if that's a line what's the equation for it?

Answer 6

Hello?

Answer 7

sorry i've never used this site before.
would it be y=.6x?

Answer 8

yes, well... Q= .6*t

Answer 9

ok now
we want the next part to be exponential and at t=1 it should = .6 ...

Answer 10

and at t=2 it should equal .998*.6

Answer 11

agree so far?

Answer 12

yeah that makes sense

Answer 13

\[.6*e ^{C(x-1)}\]
is the easiest way to express that...

Answer 14

whoops I used 'x' too!
\[.6*e ^{C(t-1)}\]

Answer 15

Where C is some constant we need to determine still...

Answer 16

do you see where this is going?

Answer 17

would c be the percent?

Answer 18

no, it's the rate of decay... we use the percent to find it...

\[.998 = e ^{C(t-1)} \]
when t=2

Answer 19

solve to find C :)

Answer 20

so its .002. Thank you so much for helping me!

Answer 21

-.002002

Answer 22

yeah thats what i meant. i forgot to type the -

Answer 23

Ok:) questions?

Answer 24

no that covers it. thanks!

Answer 25

Sure!