A second study of the country in Exercise 54 indicates that natural restrictive forces are at work that make the actual rate of growth

instead of the exponential rate P'₁(t) = 10e^0.02t. If this rate is correct, how much smaller will the population be in the year 2015 than if the exponential rate were correct?

Data from Exercises 54

The population of a third-world country grows exponentially at the unsustainable rate of P'₁(t) = 10e^0.02t thousand people per year where t is the number of years after 2005. A study indicates that if certain socioeconomic changes are instituted in this country, then the population will instead grow at the restricted rate P'₂(t) = 10 + 0.02t + 0.002t² thousand people per year. How much smaller will the population of this country be in the year 2015 if the changes are made than if they are not?

P3(t) = 20e0.02t 1 + 0.021