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
click here to see the step by step solution of the equation
After 19.44 hours there will be 10 mg of caffeine in your system.