Question

Differential equations

1. In many states in the USA it is illegal to drive with an alcohol level greater than 0.10 percent (one part of alcohol per 1000 parts of blood). Suppose someone is arrested in one of these states and is found to have a 0.8% blood alcohol percentage. Assuming that the percentage of alcohol in the bloodstream decreases proportionally to the percentage of alcohol, and that the alcohol concentration also decreases 10 percent every hour, determine how much time in hours must pass for that person to legally drive from new.

2. To an RC series circuit, in which the resistance is 1000 Ω and the capacitance is 5 × 10 ^ (- 6) F, a voltage or voltage of 200 volts is applied. Find the charge q (t) on the capacitor if i (0) = 0.4 A.
Determine the charge and current for t = 0.002 seconds and the charge when t → ∞.

3. A naphthalene cube is considered to decay at a rate proportional to its surface. A naphthalene cube that originally had a 19/2 inch side has been found to be 5/12 inch after a month. Determine the time in months for the cube to disappear.

THANKS

Answer 1