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:

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column