A person drinks a cup of coffee with 100mg of caffeine.

A person drinks a cup of coffee with 100mg of caffeine. Caffeine has a half-life of 5.7 hours. 1. Write a formula for the amount of caffeine left in the persons body t hours later.2. Find the amount of caffeine left after 8 hours.3. When will there be less than 20mg of caffeine left in the persons body?

Solution

Gen equation : y(t) = Ae^(-kt)

A = 100 mg ; y = 100e^(-kt) ; t1/2 = 5.7 hrs

T calculate k ; 50 = 100e^(-5.7k)

0.2 = e^(-5.7k)

ln(0.2) = -5.7k

k = 0.282

Formula for amount of caffene left : █(██) = ███████^(█████████████)

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█████████████████ █████████████ █████████ ███████ ████ ████ ; █ =█

██████&████; █████████^(█████████) ; ████(███████) &███; █████████████

███ &████; ███████ █████