The half-life of caffeine in a healthy adult's bloodstream is 5.7 hours. Suppose Alex, a healthy adult, drinks a Grande Latte, which contains 150 mg of caffeine, at 3 p.m. (assume, perhaps unrealistically, all of the caffeine absorbed into -kt Alex's bloodstream immediately). Use the exponential decay model A(t) = A, where t is the time since 4 p.m. measured in hours and A(t) is the amount of caffeine in Alex's bloodstream at time t. a) Find the exponential decay rate, k, for the caffeine in Alex's bloodstream. (Round to the fourth decimal place.) b) At what point in the night will there be only 50 mg of caffeine in Alex's bloodstream? (State your answer as the time to the nearest minute). c) Make a table of the values of A(t) at times t = 0,3,9, and 12. d) Sketch the graph of A(t) over the interval 0

A radioactive substance decays from 50 mg to 14 mg in 28 years according to the exponential decay model y = ae-bz, where a is the initial amount and y is the amount remaining after x years. Find the b -value. Round to the nearest hundredth, if needed. Use the EXACT b-value to write the exponential decay model for this substance with initial amount 50 mg. Use that model to find the half-life. Round to the nearest hundredth of a year, if needed. half-life years

If the population of a Nigeria doubles in 9 years, find the growth rate k. Assume that the population increases exponentially.

A material has an initial of 15 units. Which equation models the amount of the material y, decaying exponentially at a rate of 23% over time x