After drinking, the body eliminates 35% 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 n+1 = f(n). where an is the number of grams of alcohol in the body after 7 hours. Give the updating function f (as a function of the variable). Answer: f(x) = b) Peter had three alcoholic drinks that brought the alcohol content in his body to 50 grams, and then he stopped drinking. Give the initial condition (in grams) for the DTDS in (a). Answer: 0 grams e) Find the solution of the DTDS in (a) with the initial condition given in (b). (Your answer will be a function of the variable 72, which represents time in hours.) Answer: n 85 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.

During the first part of a trip, adrian drove 36 miles at a certain speed. adrian drives another 36 miles on the second part of the trip at a speed of 10 mph faster. driving time for the entire trip was 91 mins. find the rate at which adrian drove during the first part of the trip.  please help explain.

3 pipes can be used to fill up a swimming pool with water. It takes 9 mins for pipe A to fill up the pool while 6 mins for pipe B. A third pipe C, takes 4 mins to empty the pool. How long would it take to fill up the pool given these conditions?

You are driving at 60 miles per hour. If you decrease the time it takes you to travel 1 mile by 5 seconds, what is your new speed?