Michael just drank a cup of coffee to him stay awake. the coffee had 110 milligrams of caffeine in it. if his body processes 5% of the caffeine every hour, how much will be left in 8 hours?
a. 74
b. 73
c. 72
d. 56

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

,

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,

,

,

(approx)

Thus, 73 milligrams of caffeine will be left in 8 hours.

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

hope this is what you were asking for!

step-by-step explanation:

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