The amount of caffeine in the bloodstream decreases by 29% every hour. a. A cup
ID: 2891456 • Letter: T
Question
The amount of caffeine in the bloodstream decreases by 29% every hour. a. A cup of coffee contains 92 mg of caffeine. Define a function, f that gives the amount of caffeine remaining in the blood stream t hours after the coffee was consumed. Preview b. How many hours will it take for the amount of caffeine to reach half of the amount in the initial cup of coffee? hours Preview c. A double shot of espresso contains 126 mg of caffeine. Define a function, g, that gives the amount of caffeine remaining in the blood stream x hours after the espresso was consumed. Preview d. How many hours will it take for the amount of caffeine to reach half of the amount in the initial espresso? hours Preview A can of Rock Star energy drink has 180 mg of caffeine in it. How long after you consume the Rock Star will the caffeine in your blood stream decrease to 90 mg? e.Explanation / Answer
general decay equation is A(t)=A(0) e-rt where A(t) is amount after time t , A(0) is initial amount , r is rate of decay
r =29%
=>r=29/100
=>r=0.29
initial amount =92mg
a)
f(t)=92e-0.29t
==================================================
b)
half the amount is (92/2) =46 mg
=>92e-0.29t =46
=>e0.29t =92/46
=>e0.29t =2
=>0.29t=ln2
=>t=(1/0.29)ln2
=>t=2.39
it takes 2.39 hours
=============================================
c)
for expresso initial amount =126 mg
g(x)=126e-0.29x
=================================
d)
half the amount is (126/2) =63 mg
=>126e-0.29t =63
=>e0.29t =126/63
=>e0.29t =2
=>0.29t=ln2
=>t=(1/0.29)ln2
=>t=2.39
it takes 2.39 hours
==============================================
e)
90mg is half of 180mg
it takes 2.39 hours for the caffine to decreases to 90mg (half time is indepemdant of initial amount)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.