The rate of a is propothonal to the amount of the drug available for the process.
The rate of change of the amount of the drug (A) involved in a :
If you have $100 and you decided to spend 10% of what you have every day.
This is a first-order spending. The rate of spending is proportional to the amount of money remaining.
| Day |
Rate of spending |
Amount Remaining |
| 1 |
10 |
90 |
| 2 |
9 |
81 |
| 3 |
8.1 |
72.9 |
| 4 |
7.29 |
65.61 |
| 5 |
6.56 |
59.05 |
| 6 |
5.9 |
53.15 |
Notice that the fraction of money spent per day is constant (10%), however the rate of spending changes depending on the amount of money remaining.
Integration of the equation above and mathematical manipulation to obtain an equation for the amount versus time yields:
This is the equation for the amount of the drug (A) at any time t, if the for the process is k and the initial amount of the drug is A0.
Taking the natural logarithm for both sides of the first-order equation yields:
A plot of ln A versus t on yields a straight line. The y-intercept is equal to ln A0 and the is equal to -k.
