Question

Michael just drank a cup of coffee to help 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

Answer 1

The answer would be 74

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

Answer 2

73 milligrams of caffeine will be left in 8 hours.

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* 0.664`

`\Rightarrow A=72.97=73`(approx)

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