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
[tex]A=P(1-r)^n[/tex],
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,
[tex]A=110(1-0.05)^8[/tex],
[tex]\Rightarrow A=110(0.95)^8[/tex],
[tex]\Rightarrow A=110\times 0.664[/tex]
[tex]\Rightarrow A=72.97=73[/tex](approx)
Thus, 73 milligrams of caffeine will be left in 8 hours.
Answer:
The answer would be 74
Step-by-step explanation:
You have to set up a expoential decay equation. P(t)=pe^-rt
P(t)=answer
P=initial number (110)
r= rate of decay (5% or 0.05)
t= time(8)
E= 2.7183 ( number used for every equation
Equation= P(t)=110(2.7183)^-0.4 ( get -0.4 from multiplying 0.05 x 8)
1. Solve 2.7183^-0.4 =0.67031825
2. multiply 0.67031825(e) x 110(p) = 73.7350075
3. round 73.7350075 to get 74
answer is A. 74
