Question

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

Answer 1

`1.31mg`

Explanation:

`A=A_0e^(-kt)`
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=5e^(-k)`

`4/5=e^(-k)`

`In(4/5)=-k`

`k=-In(4/5)`

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

When `t=6`,

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

`A=1.31`