Jacob's body metabolizes caffeine at a rate of 13.5% per hour.
a)Jacob's body will takes 4.77 ~5 hours to metabolize half of the 96 mg of caffeine.
b) If Jacob consumes an energy drink with 212 mg of caffeine in it, Jacob's body will take 4.77948 ~ 5 hours to metabolize half of the 212 mg of caffeine.
c) Jacob consumes a cup of coffee with c mg of caffeine in it. Jacob's body will take 4.77948~ 5 hours to metabolize half of the c mg of caffeine.
The volume will slowly decrease at regular intervals and at a regular rate. This growth reduction is calculated using the exponential decay formula. The general form is y = a(1- r)ᵗ
We have, decay rate r = 13.5 % = 0.135
Initial value , a = 96 mg
plugging the value in formula we get,
y = 96(1 - 0.135)ᵗ --(1)
Now, Half of 96 is 48
so, 48 = 96(0.865)ᵗ --(2)
dividing equation by 96 we get
=> 48/96 = (0.865)ᵗ
taking natrual logarithm both sides,
=> ln(1/2) = ln ((0.865))
=> ln(1/2) = t In (0.865)
=> t = ln(1/2)/In (0.865)
=> t = 4.77948
Since, decay rate is constant so, half never changes for any .
a) 4.779~5 hours, long will it take for Jacob's body to metabolize half of the 96 mg of caffeine.
b) Jacob's body to metabolize half of the 212 mg of caffeine is 4.779~ 5 hours.
c) for Jacob's body to metabolize half of the cmg of caffeine is 4.77948.. So, we have 4.77948 ~ 5 hours is decay constant rate.
To learn more about Decay rate , refer:
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