Question

I need help with my homework please it’s a two part question

Answer 1

Given

The therapeutic drug prescribed by the doctor is 225 milligrams.

It is decayed by 40 percent each hour.

Explanation

Use the exponential equation.

`A(t)=A_o\left(1−r\right)^t`

Substitute the values,

`A(t)=225(1-0.4)^t^`
`A(t)=225(0.6)^t`

To determine the half life of the drug,

`\begin{gathered} (225)/(2)=225(0.6)^t \\ (1)/(2)=0.6^t \\ 0.5=0.6^t \end{gathered}`

Take ln both sides and find t,

`\begin{gathered} ln0.5=tln0.6 \\ t=(ln0.5)/(ln0.6) \\ t=(-0.69314)/(-0.51082) \\ t=1.357 \end{gathered}`

Answer

To the nearest hundredth , the half life of the drug is 1.36 hour.

b. The amount of therapeutic drug left after 10 hours is

`\begin{gathered} A(10)=225(0.6)^(10) \\ A(10)=1.36mg \end{gathered}`

Hence the amount of therapeutic drug left after 10 hours is 1.36 mg.