Question

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(t) = 0.0225te−0.0467twhere t is measured in minutes after consumption and C is measured in mg/mL.how rapidly was the BAC increasing after 5 minutes

Answer 1

Answer:

After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.

Step-by-step explanation:

The average blood alcohol concentration (bac)  is modeled by the following function.

$c(t) = 0.0225te^{-0.0467t}$

In which t is measured in minuted.

How rapidly was the BAC increasing after 5 minutes?

This is c'(t) when t = 5.

Using the derivative of the product.

Derivative of the product:

$c(t) = f(t)*g(t)$

$c'(t) = f'(t)*g(t) + f(t)*g'(t)$

In which problem:

$f(t) = 0.0225t$

$g(t) = e^{-0.0467t}$

So

$c'(t) = 0.0225e^{-0.0467t} - 0.0225*0.0467*te^{-0.0467t}$

$c'(5) = 0.0225e^{-0.0467*5} - 0.0225*0.0467*5e^{-0.0467*5} = 0.0137$

After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.