Question

After drinking, the body eliminates 36% of the alcohol present in the body per hour. a) The amount of alcohol in grams in the body on an hourly basis is described by a discrete time dynamical system (DTDS) of the form $x_{n+1} = f(x_n)$, where $x_n$ is the number of grams of alcohol in the body after $n$ hours. Give the updating function $f$ (as a function of the variable $x$). Answer: $f(x) = 0.64x$ b) Peter had three alcoholic drinks that brought the alcohol content in his body to 42 grams, and then he stopped drinking. Give the initial condition (in grams) for the DTDS in (a). Answer: $x_0 = 42$ grams c) Find the solution of the DTDS in (a) with the initial condition given in (b). (Your answer will be a function of the variable $n$, which represents time in hours.) Answer: $x_n = 65.625$ d) If the amount of alcohol in Peter's body has to be below 8 grams before one can drive, how long (in hours) does Peter have to wait before he can drive? Round up to the nearest integer value. Answer: 8 hours

          After drinking, the body eliminates 36% of the alcohol present in the body per hour.
a) The amount of alcohol in grams in the body on an hourly basis is described by a discrete time dynamical system (DTDS) of the form $x_{n+1} = f(x_n)$, where $x_n$ is the number of grams of alcohol in the body after $n$ hours. Give the updating function $f$ (as a function of the variable $x$).
Answer: $f(x) = 0.64x$
b) Peter had three alcoholic drinks that brought the alcohol content in his body to 42 grams, and then he stopped drinking. Give the initial condition (in grams) for the DTDS in (a).
Answer: $x_0 = 42$ grams
c) Find the solution of the DTDS in (a) with the initial condition given in (b). (Your answer will be a function of the variable $n$, which represents time in hours.)
Answer: $x_n = 65.625$
d) If the amount of alcohol in Peter's body has to be below 8 grams before one can drive, how long (in hours) does Peter have to wait before he can drive?
Round up to the nearest integer value.
Answer: 8 hours

After drinking, the body eliminates 36% of the alcohol present in the body per hour.
a) The amount of alcohol in grams in the body on an hourly basis is described by a discrete time dynamical system (DTDS) of the form xn+1 = f(xn), where xn is the number of grams of alcohol in the body after n hours. Give the updating function f (as a function of the variable x).
Answer: f(x) = 0.64x
b) Peter had three alcoholic drinks that brought the alcohol content in his body to 42 grams, and then he stopped drinking. Give the initial condition (in grams) for the DTDS in (a).
Answer: x0 = 42 grams
c) Find the solution of the DTDS in (a) with the initial condition given in (b). (Your answer will be a function of the variable n, which represents time in hours.)
Answer: xn = 65.625
d) If the amount of alcohol in Peter's body has to be below 8 grams before one can drive, how long (in hours) does Peter have to wait before he can drive?
Round up to the nearest integer value.
Answer: 8 hours

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