Medical science soon after an injection, the concentration d (in milligrams per milliliter) of a drug in a patient's bloodstream is 500 milligrams per milliliter. after 6 hours, 50 milligrams per milliliter of the drug remains in the bloodstream.
(a) find an exponential model for the concentration d after t hours.
(b) what is the concentration of the drug after 4 hours?

a)

b) For this case we just need to replace t=4 and see what we got:

Step-by-step explanation:

For this case the proportional model is given by the following differential equation:

Where D is the concentration, t the time and k a proportional constant.

We can rewrite the differential equation like this:

And if we integrate both sides we got:

Part a

And if we apply exponentiation on both sides we got:

So then our model is given by:

Where is the initial amount for t =0.

For this case we have the initial condition assumed:

So then our model is given by:

We have another condition given:

If we divide both sides by 500 we got:

And if we apply natutral log on both sides we got:

And our model then is given by:

Part b

For this case we just need to replace t=4 and see what we got:

529 and 531

step-by-step explanation: