Question

The number of milligrams of a drug that remains in a patient's system after t hours is given by the function A(t) = Iert. Ted was given 200 milligrams of medicine which leaves his bloodstream at a rate of 20%. How much of the medicine remains in his system after 4 hours?

Answer 1

For exponential decay the function should be written as follows:
\[A(t)=Ie ^{-rt}...........(1)\]
where A is the amount after time t hours, r is the rate of decay per hour a a decimal and I is the initial amount.
You need to plug the given values into equation (1).

Answer 2

as a decimal*

Answer 3

Here was the work I did for it, but it didn't match any of the answer choices.

A(t)=Ie^rt
A(t)=200e^(0.20)(4)
A(t)=200e^(0.8)
A(t)=200(2.2255)
A(t)=445.1

Answer 4

\[A=200\times e ^{-0.2\times 4}=you\ can\ calculate\]

Answer 5

A(t)=89.86. Thank you :)

Answer 6

If you look at the corrected equation that I posted you will see the the exponent of e must have a negative sign. Your calculation does not have a negative sign.

Answer 7

Right, my new answer did.

Answer 8

Your new answer is correct. You're welcome :)