Item b.)
To solve that item we must remember the general formula for exponential decay, it's
[tex]f(t)=A(1-r)^t[/tex]
Then, let's modify it to fit our parameters
A is the initial value, in our case, the initial value is the dosage, 500mg, then A = 500
r is the rate, we have 5.2%, then the value of r will be 0.052
And f(t) will transform into D, changing the name.
Hence
[tex]D=500(1-0.052)^t[/tex]
We can also simplify the subtraction, we get
[tex]D=500\cdot(0.948)^t[/tex]
Item c.)
To solve that we will use our equation, we will input t = 6 hours and find the value of D.
[tex]\begin{gathered} \begin{equation*} D=500\cdot(0.948)^t \end{equation*} \\ \\ D=500\cdot(0.948)^6 \\ \\ D=500\cdot0.726 \\ \\ D=363\text{ mg} \end{gathered}[/tex]
The answer is 363 mg
