Module 5.2: unconstrainedError

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The Unconstrained Growth Error model takes into account the difference in population that occurs when graphing the function for growth rate versus using Euler's method to estimate population growth. Euler's method usually produces an accumulation error. This model incorporates a term, relative error percent to show the differences.

The term actual population, evaluates the initial population times the exponential growth rate. In Nova, this looks like 100*Math.exp(growth rate * TIME()). Population is initally 100, however, in another version of this model, population could easily be controlled by a slider. The term growth rate, is controlled by a slider that feeds the growth flow into the population stock.

The relative error percent computes the relative error as the absolute value of the difference in Euler's estimate and the actual population. This equation looks like this in Nova: Math.abs(population - actual_population) * 100/actual_population.

The graph shows the population as estimated by Euler's Method and the actual population over time. The differences are minuscule in the beginning, but as time goes on, they become much greater.