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,

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

Take ln both sides and find t,

$\begin{gathered} ln0.5=tln0.6 \\ t=\frac{ln0.5}{ln0.6} \\ t=\frac{-0.69314}{-0.51082} \\ t=1.357 \end{gathered}$

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.