Question

Carlos has taken an initial dose of a prescription medication.

Answer 1

Answer:

3.48 hours

Step-by-step explanation:

The equation is:

$M(t)=20 e^{-0.86t}$

Where

M(t) is the amount of medication remaining in mg

t is the time it takes, in hours

The questions asks HOW LONG it will take to make the remaining medication to 1 milligrams (1 mg)??

We have to substitute M(t) with "1" and find the corresponding value of "t". We will use natural log to solve this. Shown below:

$M(t)=20e^{-0.86t}\\1=20e^{-0.86t}\\0.05=e^{-0.86t}\\Ln(0.05)=Ln(e^{-0.86t})\\Ln(0.05)=(-0.86t)Ln(e)\\t=\frac{Ln(0.05)}{-0.86}\\t=3.48$

Note: Ln(e) = 1

This means, the amount of time it will take is about 3.48 hours