I'm not sure how to solve a or b. I do know that this involves solving the DE with initial conditions. I also know that B(0)= 0.12 and B(7.5)= 0. B being BAC%, and t being time in hours.
Here is the actual math problem:
In many states it is illegal to drive with a blood alcohol level greater than 0.08% (eight parts alcohol per ten-thousand parts of blood). A BAC (blood alcohol content) calculator online stated that a 140 lb. adult who consumes 5 drinks (defined in the program) in a 3 hour period will have a blood alcohol level of 0.12 g alcohol/ 100ml blood (a BAC of .12%). This program uses a linear model to calculate that there will be no alcohol left in the blood in 7.5 hours.
a. Set up and solve an IVP to determine the percentage of alcohol in the bloodstream at any value of time t (t > 0)-- Use the simplistic assumption that the rate at which alcohol is removed from the blood is constant. Remember to start with a DE and initial value. Use your second value to find a rate constant (slope).
b. Set up and solve an IVP to determine the percentage of alcohol in the bloodstream at an value of time t, (t > 0) , but this time assume that the rate at which BAC drops is proportional to the amount of alcohol currently in the blood at time t. This is supposed to be a more realistic model of BAC for time t. Be sure and give your growth rate constant exactly or with at least 6 decimal places.
Here is the actual math problem:
In many states it is illegal to drive with a blood alcohol level greater than 0.08% (eight parts alcohol per ten-thousand parts of blood). A BAC (blood alcohol content) calculator online stated that a 140 lb. adult who consumes 5 drinks (defined in the program) in a 3 hour period will have a blood alcohol level of 0.12 g alcohol/ 100ml blood (a BAC of .12%). This program uses a linear model to calculate that there will be no alcohol left in the blood in 7.5 hours.
a. Set up and solve an IVP to determine the percentage of alcohol in the bloodstream at any value of time t (t > 0)-- Use the simplistic assumption that the rate at which alcohol is removed from the blood is constant. Remember to start with a DE and initial value. Use your second value to find a rate constant (slope).
b. Set up and solve an IVP to determine the percentage of alcohol in the bloodstream at an value of time t, (t > 0) , but this time assume that the rate at which BAC drops is proportional to the amount of alcohol currently in the blood at time t. This is supposed to be a more realistic model of BAC for time t. Be sure and give your growth rate constant exactly or with at least 6 decimal places.