Answer:
73 milligrams of caffeine will be left in 8 hours.
Step-by-step explanation:
Given:Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it.
Also, his body processes 5% of the caffeine every hour.
We have to find how much caffeine will be left in 8 hours.
Since, the amount of caffeine is decreasing in body, we can use decay formula
\(A=P(1-r)^n\),
where A is the amount left after n time
P is initial amount
r is rate of decay
n is time
Given : P = 110 , r = 5% , t= 8 hours.
Substitute , we get,
\(A=110(1-0.05)^8\),
\(\Rightarrow A=110(0.95)^8\),
\(\Rightarrow A=110\times 0.664\)
\(\Rightarrow A=72.97=73\)(approx)
Thus, 73 milligrams of caffeine will be left in 8 hours.
