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
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
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Transcribed Image Text: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
Alex's bloodstream immediately). Use the exponential decay model A(t) = A, e
-kt
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 <t < 12.
e) If Alex wakes up the next morning and drinks another Grande Latte at 8 am, how much caffeine will be in Alex's
system at that point? (Round to the nearest tenth of a milligram.)
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