You drink a beverage with 84mg of caffeine. Each hour , the caffeine in your system decreases by about 8%. How long until you have 10mg of caffeine?

Question

You drink a beverage with 84mg of caffeine. Each hour, in your system decreases by about 8%. How long until you have 10mg of caffeine?

Answer 1

8/84 = 0.92^t

0.0952 = 0.92^t

log 0.0952 = t log 0.92

-1.02 = -0.036 t

t = 28.3 hours