Visions of Mathematics: Algebra

Laws of growth & decay

1. Linear Expansion   $l = l_0e^{\alpha\theta}$

2. Change in electrical resistance with temperature   $R_\theta = R_0e^{\alpha\theta}$

3. Tension in belts $T_1 = T_0e^{\alpha\theta}$

4. Newton's law of cooling $\theta = \theta_0e^{-kt}$

5. Biological growth   $y = y_0 e ^{kt}$
6. Discharge of a capacitor $q = Qe^{-\tfrac{t}{CR}}$

7. Atomsphere pressure $p = p_0 e ^{-\frac{h}{c}}$

8. Decay of current in an inductive circuit $i= I e ^{-\frac{Rt}{L}}$

9. Growth of current in a capacitive circuit $i= I (1- e ^{-\frac{t}{CR}})$