Answer:
B. 106.2
Step-by-step explanation:
We have been given that at 7 am you drink a 12-ounce cup of coffee which has 140 mg of caffeine. The liver metabolizes caffeine at a rate of 12.9% per hour. We are asked to find the milligrams of caffeine left in your body after 2 hours.
We will use exponential decay formula to solve our given problem.
[tex]y=a\cdot (1-r)^x[/tex], where,
y = Final value,
a = Initial value,
r = Decay rate in decimal form,
x = Time.
Let us convert 12.9% in decimal form.
[tex]12.9\%=\frac{12.9}{100}=0.129[/tex]
Initial value is 140 mg.
[tex]y=140\cdot (1-0.129)^x[/tex]
[tex]y=140\cdot (0.871)^x[/tex]
Now we will substitute [tex]x=2[/tex] in our equation as:
[tex]y=140\cdot (0.871)^2[/tex]
[tex]y=140\cdot (0.758641)[/tex]
[tex]y=106.20974\approx 106.2[/tex]
Therefore, approximately 106.2 milligrams of caffeine will be in your body after 2 hours.
