Respuesta :
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.
[tex]c(t) = 0.0225te^{-0.0467t}[/tex]
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:
[tex]c(t) = f(t)*g(t)[/tex]
[tex]c'(t) = f'(t)*g(t) + f(t)*g'(t)[/tex]
In which problem:
[tex]f(t) = 0.0225t[/tex]
[tex]g(t) = e^{-0.0467t}[/tex]
So
[tex]c'(t) = 0.0225e^{-0.0467t} - 0.0225*0.0467*te^{-0.0467t}[/tex]
[tex]c'(5) = 0.0225e^{-0.0467*5} - 0.0225*0.0467*5e^{-0.0467*5} = 0.0137[/tex]
After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.
