Question

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?

Answer 1

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

Answer: 15 hours (rounded to the nearest whole hour)