You drink a beverage with 145 mg of caffeine. each hour, the caffeine in your system decreases by about 12 percent. how long until you have 21mg of caffeine?

You can write the function for the amount of caffeine in your system as:

c(t) = 145 * (1 - 0.12)^ (t) = 145 * (0.88)^t

Then, you want to find t when c(t) = 21

=> 21 = 145 * (0.88)^t

=> 21/145 = (0.88)^t

Which applyin logarithm properties => t * log (0.88) = log (21/145)

=> t = [log 21/145)] / [log 0.88)] = 15.11 hours ≈ 15 hours

15 hours (rounded to the nearest whole hour)