(6 pts) Most of the Western European countries are having a dramatic decline in their growth rate to the point where the

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6 Pts Most Of The Western European Countries Are Having A Dramatic Decline In Their Growth Rate To The Point Where The 1 (471.62 KiB) Viewed 61 times

(6 pts) Most of the Western European countries are having a dramatic decline in their growth rate to the point where their populations will actually begin to decline early in this century. Consider the case of Austria. Its population was 6.93 million in 1950, 7.47 million in 1970, and 7.71 million in 1990. a. Use the nonautonomous Malthusian growth model given by dP dt (b – at)P, P(0) = 6.93. Lett be the number of years after 1950, then solve this differential equation. P(t) = where this solution includes the parameters a and b along with the independent variable t. Use the population data for Austria to find the constants a and b. a = b= b. The population for Austria was 8.12 million in 2000. Use the model above to estimate the population of Austria, then compute the percent error from the actual census data. Predicted population in 2000 = (million) Percent Error = c. When does the model predict that Austria will have its largest population (value of t) and what is that population? Time of Max Population = (years afer 1950). Maximum population = (million)