Problema Solution

you drink a beverage with 120mg of caffeine. Each hour the caffeine in your system decrease about 12% How long until you have 10mg of caffeine?

Answer provided by our tutors

start: 120 mg caffeine


after 1 hour: 120 - 0.12*120 = 120(1 - 0.12)


after 2 hours: 120(1 - 0.12) - 0.12*120(1 - 0.12) = 120(1 - 0.12)^2


after 3 hours: 120(1 - 0.12)^3


after n hours: 120(1 - 0.12)^n


we need to find n so that 120(1 - 0.12)^n = 10


by solving the equation


120(1 - 0.12)^n = 10


0.88^n = 1/12


n = 19.44 hours


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After 19.44 hours there will be 10 mg of caffeine in your system.