Respuesta :
Answer:
(a) The 5-hour decay factor is 0.5042.
(b) The 1-hour decay factor is 0.8720.
(c) The amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.
Step-by-step explanation:
The amount of caffeine in Chase's body decreases exponentially.
The 10-hour decay factor for the number of mg of caffeine is 0.2542.
The 1-hour decay factor is:
[tex]1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720[/tex]
(a)
Compute the 5-hour decay factor as follows:
[tex]5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042[/tex]
Thus, the 5-hour decay factor is 0.5042.
(b)
The 1-hour decay factor is:
[tex]1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720[/tex]
Thus, the 1-hour decay factor is 0.8720.
(c)
The equation to compute the amount of caffeine in Chase's body is:
A = Initial amount × (0.8720)ⁿ
It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.
Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:
[tex]A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112[/tex]
Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.
