Part 1:
Let
Q₁ = Amount of the drug in the body after the first dose.
Q₂ = 250 mg <span>As we know that after 12 hours about 4% of the drug is still present in the body.
For Q</span>₂<span>,
we get:
Q</span>₂ = 4% of Q₁ + 250
= (0.04 × 250) + 250
= 10 + 250
= 260 mgTherefore, after the second dose, 260 mg of the drug is present in the body.
Now, for Q₃ :
<span>We get;
Q</span>₃ = 4% of Q2 + 250
= 0.04 × 260 + 250
<span> = 10.4 <span>+ 250
= 260.4</span></span><span><span>For Q₄,
We get;
Q₄ = 4% of Q₃ + 250
= 0.04 × 260.4 + 250
= 10.416 + 250
= 260.416
</span><span>
Part 2:
To find out how large that amount is, we have to find Q₄₀.
Using the similar pattern
for Q₄₀,
We get;
Q₄₀ = 250 + 250 × (0.04)¹ + 250 × (0.04)² + 250 × (0.04)³⁹
Taking 250 as common;
</span></span> Q₄₀ =<span> 250 (1 + 0.04 + 0.042 + ⋯ + 0.0439)
<span> = 2501 − 0.04401 − 0.04
</span> </span>
Q₄₀ = 260.4167
Hence,
T<span>he greatest amount of antibiotics in Susan’s body is
260.4167 mg.
Part 3:
</span>From the previous 2 components<span> of </span>the matter, we all know<span> that </span>the best quantity<span> of the antibiotic in Susan's body is </span>regarding <span>260.4167 mg and </span>it'll<span> occur right </span>once<span> she has taken the last dose. However, </span>we have a tendency to<span> see that already </span>once<span> the fourth dose she had 260.416 mg of the drug in her system, </span>that is simply<span> insignificantly smaller. </span>thus we will<span> say that </span>beginning<span> on the second day of treatment, </span>double every day there'll<span> be </span>regarding<span> 260.416 mg of the antibiotic in her body. Over the course of </span>the subsequent twelve<span> hours {the </span>quantity<span>|the quantity|the number} of the drug </span>can<span> decrease to 4%</span><span> of </span>the most amount<span>, </span>that<span> is 10</span><span>.4166 mg. Then the cycle </span>can<span> repeat.</span>
