2 VocabularyAn exponential decay function has the form y = abx, where a > 0 and 0 < b < 1.The base b of an exponential function is called the decay factor.The time required for a substance to fall to half its initial value is called half-life.
6 Vocabulary Exponential Decay Model The amount y of the quantity after t years can be modeled by the equation y = a(1 – r)t, where a is the initial amount and r is the percent decrease expressed as a decimal.Note that the quantity 1 – r is the decay factor.
7 Example 4:The rate at which caffeine is eliminated from the bloodstream is about 15% per hour. An adult drinks a caffeinated soda, and the caffeine in his or her bloodstream reaches a peak level of 30 milligrams.Predict the amount, to the nearest tenth of a milligram, of caffeine remaining 1 hour after peak and 4 hours after the peak level.
8 Solution:In growth to obtain the growth factor we added our rate, so exponential decay we _________ the rate of decay from 100%.What is our decay factor?Write the expression for the caffeine level x hours after the peak level.30(.85)x85% or 0.85
9 Solution continued:What is the amount of caffeine remaining after 1 hour?25.5 milligramsAfter 4 hours?15.7 milligrams