OtherApps+of+DiffEqns


 * Other Types of Growth and Decay **

When money is invested or borrowed compount interest is used. The rate at which the investment or borrowed amount grows at is proportional to the Principal, P (amount invested). So: math \dfrac{dP}{dt}=Pr math
 * Compound Interest**

Where r is the interest rate as a decimal.

Atmospheric pressure drops with an increase in height above sea level such that
 * Pressure, Light intensity etc**

math \dfrac{dP}{dh} =-kP math Light intensity drops as it passes through a medium in a similar way.

Growth does not need to be proportional to a linear term as above. We could just as easily have the growth of bacteria in a petri dish given by:
 * Non-linear proportions**

math \dfrac{dP}{dt}=k\sqrt{P} math These are solved the same way as previous examples, the integral to solve will just be different.

Sometimes growth will occur but some part of the population is removed each year. For example a Alpaca farmer might increase his flock of 200 by 15% each year but sell 5 to other farmers. In this case we can set up the differential equation:
 * Population with regular removal**

math \dfrac{dP}{dt}=kP-5 \\ \text{k must be 0.15 as it grows by 15%} \\ \text{so} \\ \dfrac{dP}{dt}=0.15P-5, \text{ given }P(0)=200 \\ math This can then be solved as normal.