9. -12 points SCalcET8 3 4085 The average blood alcohol concentration (BAC) of e

Question

9. -12 points SCalcET8 3 4085 The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption of 15 mL of ethanol (corresponding to one alcoholic drink). The resulting data were modeled by the concentration function C() 0.0225te-0.0467t where t is measured in minutes after consumption and C is measured in mg/mL. (Round your answers to five decimal places.) (a) How rapidly was the BAC increasing after 5 minutes? (mg/mL)/min b) How rapidly was it decreasing half an hour later (t30)7 (mg/mL)/min

Explanation / Answer

given C(t)=0.0225te-0.0467t

=>C'(t)=0.0225(1e-0.0467t -0.0467te-0.0467t )
=>C'(t)=0.0225(1-0.0467t)e-0.0467t

a)

after 5minutes, t=5
rate =C'(5)
=>rate =0.0225(1-0.0467*5)e-0.0467*5
=>rate =0.01365

BAC increasing at 0.01365 (mg/mL)/min

b)

after half an hour, t=30
rate =C'(30)
=>rate =0.0225(1-0.0467*30)e-0.0467*30
=>rate =-0.00222

BAC decreasing at 0.00222 (mg/mL)/min

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