7,728.4 in word form
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It will take 7.5 hours for only 40% of the caffeine to remain in his body.
Step-by-step explanation:
Half-life (symbol t1⁄2) is the time required for a quantity to reduce to half of its initial value.
The half-life of caffeine is 5.7 hours.
It means that if we have 10 ounces of caffeine. After 5.7 hours, the remaining caffeine will be equal to 5 ounces and so on.
And the decaying speed depends on the initial amount of the substance.
In the given question.
t1⁄2 = 5.7 hours
Initial amount = N(i) = 16 ounces
Remaining amount after time t = N(t) = 40% of 16 = 6.4 ounces
time t = ?
Using the following formula for remaining amount of substance after time t:
N(t) = N(i)*(0.5)^(t/t1⁄2)
we can find the time t
putting the values in the formula given above, we get:
Taking natural log on both sides:
Learn more about Half-life from brainly.com/question/12341489
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