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Curt just drank a cup of coffee to help him stay awake. The coffee had 130 milligrams of caffeine in it. If his body processes 7% of the caffeine every hour, how much will be left in 4 hours?

Verified Answer :

maroondreams

After 4 hours, his body will have processed 28% because 74 = 28. But, you're trying to find what's left (so, subtract that % from 100)

100%-28% = 72%

Then multiply the percent left by the total number of milligrams of caffeine

130.72 = 93.6 mg

JeanaShupp

Answer: 97.25 milligrams

Step-by-step explanation:

Given: Curt just drank a cup of coffee to help him stay awake.

The initial amour of caffeine in coffee= 130 milligrams

The rate of decay of caffeine in body = 7%= 0.07

We know that the exponential decay equation with rate r and and time t is given by :-

\(f(x)=A(1-r)^t\), where A is the initial value.

Now, the amount of caffeine left in body after 4 hours is given by :-

\(f(4)=130(1-0.07)^4\\\\\Rightarrow\ f(4)=97.2467613\approx97.25\text{ milligrams}\)

Hence, after 4 hours 97.25 milligrams will be left.

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