Population Growth
Differential equations are useful for finding a formula for the population of people, animals, and bacteria at a certain time; for example:
Figure 12.7: Differential equation to calculate population at time t
This differential equation means the rate of change of y is proportional to y, or the population grows proportional to its amount. This is the definition of population growth rate: a fraction or percentage of the population. The solution is similar to our interest problems involving continuous compounding:
Figure 12.8: Differential equation to calculate the rate of change
Exercise 12.06: Calculating the Population Growth Rate – Part 1
In the 1980s, the annual population growth rate in Kenya was 4%. At that rate, how long would it take for the population to double? Follow these steps to complete this exercise:
- No matter what the starting population, we're looking for t, which makes the factor...
