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

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<t

anonymous · Answer

so find A(t)

anonymous · Answer

how? I know t is 1 sec

anonymous · Answer

steadily injected means its a linear (line) equation
at t=1 the dose=.6, at t=0 dose=0
(0,0) (1,.6)

anonymous · Answer

2 points so you can find a line

anonymous · Answer

ok

anonymous · Answer

finding B(t) is a bit tricky
and i really dont have the attention span atm to solve it

we know every second it decreases by .2%

anonymous · Answer

but what equation am I plugging these numbers into?

anonymous · Answer

t=1 dose = .6
t=2 dose= .6(1-.002)
t=3 dose=.6(1-.002)^2

can you make an equation for this?

anonymous · Answer

okay so after 2 second theres 0.998

anonymous · Answer

I still don't get what A(t) is

anonymous · Answer

you solve that yourself

IMPORTANT LINE RELATED EQUATIONS TO KNOW AND MEMORIZE

slope formula
m= slope/ gradiant -- same thing
$$m=\frac{y_2-y_1}{x_2-x_1}$$

standard formula
$$Ax+By=C$$

point-slope formula
$$y-y_1=m(x-x_1)$$

slope-intercept formula
b= y-intercept -- in the form of (0,y)

$$y=mx+b$$

anonymous · Answer

Can someone tell me what A(t) is I can't figure it out??