# Exponential Functions problem ?

The remaining mass, M, in milligrams of a drug in a person's bloodstream after t hours is modeled by the relation M=500(1/2)1/2.

a) what's the initial mass of the drug?

b) what's the half life of the drug?

c) what's the mass of the drug in the bloodstream after 1 day?

Any help is much appreciated!!

Update: This is the relation as the teacher gave it to me. I don't have any more info

### 3 Answers

- Wayne DeguManLv 72 months agoFavorite Answer
I would assume that you relation should be:

M(t) = 500(1/2)^t

Initial mass is when t = 0

i.e. M(0) = 500(1/2)⁰ => 500 mg

Half-life occurs when t = 1 hour

After 1 day, i.e. when t = 24 we have:

M(24) = 500(1/2)²⁴ => 0.00003 mg

or, 0.03 µg

:)>

- charlatanLv 72 months ago
M=500(1/2)1/2. should actually read

M=500*(1/2)^(t)

1/2 is half life

t= time 1/2 an hour multiples

that mean in 1/2 an hour, half of the drug is active(50%)

initial mass is 500 mg

after first (t=1)1/2 hr, 250 mg is remaining.

after two(t=2), 1/2*1/2 =1/4 of 500 mg is remaining and so on

in 24 hr 48 half hours are there

M=500*(1/2)^48

now do the computation.

did i make the problem clear to you?

- az_lenderLv 72 months ago
You've mistyped the relation. Where's the t? Is some part of the expression an exponent?