The number of milligrams of a drug that remains in a patient's system after t hours is given by the function A(t) = Ie^(rt). Juan was given 600 milligrams of medicine which leaves his bloodstream at a rate of 25%. How much of the medicine remains in his system after 6 hours?

Question

tkhunny · Answer

"25%" is not a rate.  25% per hour?

$A(t) = 600e^{rt}$

We know that $A(1) = 0.25*600 = 150$ -- This can be used to find the proper value for 'r'.  Go!

anonymous · Answer

I think it should be $$A(6)=0.25\times600=150$$

anonymous · Answer

and that approximately 150 mg of the medicine would be in his blood after 6 hours. Am I right?

tkhunny · Answer

Well, that would be part of the problem with your language.  You did not address my question about 25%.

I suspect the rate is 25% / hour, making A(1) = 150.  This equation will allow you to find 'r'.  This value for 'r' will allow you to find A(6).

tkhunny · Answer

Whoops!

The exit rate  is 25% / hour, not the remainder.
This makes A(1) = 600(1 - 25%) = 450.

Sorry about that.

anonymous · Answer

How do i use A(1)=450 to find r?

tkhunny · Answer

$A(t) = 600\cdot e^{r\cdot t}$

$A(1) = 600\cdot e^{r\cdot (1)} = 450$ - -Solve for r.