# Find an equation and use it to find the level of the drug in the blood six hours after it is taken?

## 1 tablet of medication contains 5.0 milligrams (mg) of phenylephrine. The table below shows the decay of this drug in the blood over a period of four hours after it is taken

Aug 3, 2018

$1.31 m g$

#### Explanation:

$A = {A}_{0} {e}^{- k t}$
Where
${A}_{0}$ is the initial level of phenylephrine
$A$ is the current level of phenylephrine
$t$ is the time

The $k$ is negative because it is an exponential decay

Looking at the table, we can tell ${A}_{0} = 5$

To find $k$, we know that $t = 1$, $A = 4$

$4 = 5 {e}^{- k}$

$\frac{4}{5} = {e}^{- k}$

$I n \left(\frac{4}{5}\right) = - k$

$k = - I n \left(\frac{4}{5}\right)$

A=5e^((In4/5)t

When $t = 6$,

A=5e^((In4/5)times6

$A = 1.31$