Mathematics
Joanna12
2016-04-26 20:19:12
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?
ANSWERS
HTSmith
2016-04-27 00:42:10

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)

ADD ANSWER