Exponential Equation for amount of drug in bloodstream

[Sam Squared]

Ok, so I have a question that's related to hypnotic drugs.

There's an equation for the drug that is Y = A(0.5)^x, where Y is the amount of drug in the blood (measured in µg/L), A is the initial dosage (measured in µg/L) and x is the time in hours after the drug reaches the blood.

The question is to investigate the effects of taking a 4µg dosage of this drug every hour and find an equation for it. So far this is what I've done:

0 hours

y = 4

1 hours

y = 4(0.5)^1
y = 2

y = 4(0.5)^0
y = 4

2 hours

y = 4(0.5)^2
y = 1

y = 4(0.5)^1
y = 2

y = 4(0.5)^0
y = 4

3 hours

y = 4(0.5)^3
y = 0.5

y = 4(0.5)^2
y = 1

y = 4(0.5)^1
y = 2

y = 4(0.5)^0
y = 4

From which I've been able to make this table:

0	1	2	3	   4	   5	   6
4	6	7	7.5	7.75	7.875	7.9375

I've been told that I can make a geometric series of it by someone else, that will look something like y = 8(1-(1/2)^(x+1))), but is any other ways?

Thank you.

 

[skeeter]

t = 0 ... y = 4

t = 1 ... y = 4 + 4(.5)

t = 2 ... y = 4 + [4 + 4(.5)](.5) = 4 + 4(.5) + 4(.5)²

t = 3 ... y = 4 + [4 + 4(.5) + 4(.5)²](.5) = 4 + 4(.5) + 4(.5)² + 4(.5)³

see the pattern for the geometric series?

 

[Sam Squared]

t = 0 ... y = 4

t = 1 ... y = 4 + 4(.5)

t = 2 ... y = 4 + [4 + 4(.5)](.5) = 4 + 4(.5) + 4(.5)²

t = 3 ... y = 4 + [4 + 4(.5) + 4(.5)²](.5) = 4 + 4(.5) + 4(.5)² + 4(.5)³

see the pattern for the geometric series?

ah, yes. But how do I turn that into an equation so I can graph it?

 

[skeeter]

what is the sum of a geometric series with a finite number of terms?