The country of Palladia has 3,750,000 people. The birth rate is 1.3%. That is, e

Question

The country of Palladia has 3,750,000 people. The birth rate is 1.3%. That is, each year the number of babies born is equal to 1.3% of the people in the country at the beginning of the year. The death rate is 0.7% of the people in the country at the beginning of the year. Palladia is a wealthy paradise so lots of people are trying to enter from outside. The Minister of Immigration is proposing that 150,000 people be allowed to immigrate into the country each year (a) Create a worksheet for the Minister that predicts the population of Palladia for each of the next 10 years. There should be an input area at the top of your worksheet with cells for: starting population, annual birth rate, annual death rate, and annual immigration. Use the numbers above. There should be one row for each year. There should be columns for Population at Beginning of Year, Births, Deaths, Immigration, Population at End of Year. Assume the year. (b) Suppose the birth rate is 1.1%, the death rate is 0.9%, and the annual immigration is 100,000. (c) Suppose the birth rate is 1.0% and the death rate is 0.7%. The Prime Minister would like to see close to 5,000,000 people in the country at the end of 10 years. At what number should the annual immigration quota be set? Use Goal Seek to find a quota that results in a population that is 5,000,000 in 10 years. (d) Add a one-dimensional data table that shows the size of the population in 10 years using the entered birth rate and death rate and annual immigration of 0, 10,000, 20,000 all the way through 300,000. Try the worksheet with a birth rate of 1.3% and a death rate of 0.7% (e) Add a two-dimensional data table that shows the population at the end of 10 years for birth rates of 0%, 0:1%, 0.2%, through 2.0% for the top row and annual immigration of 0, 10,000, 20,000, through 300,000 for the leftmost column. Try your worksheet with a death rate of 0.9%

Explanation / Answer

Initially population of Palladia = 3,750,000

Birth Rate = 1.3 % of 3,750,000 ==> Total Births = (1.3 * Population at the beginning of year) /100 (Round off)

Death Rate = 0.7% of 3,750,000 ==> Total Deaths = (0.7 * Population at the beginning of year) /100 (Round off)

People allowed to migrate in country = 150,000

Population at the end of year= (Population at the beginning of year) + Total Births + Total Immigrations - Total Deaths

a)

Immigrations

b)

Calculations for this can be done same as above with following data:

Initial Population = 3750000

Birth Rate = 1.3 % of 3750000 ==> Total Births = (1.1 * Population at the beginning of year) /100 (Round off)

Death Rate = 0.7% of 3750000 ==> Total Deaths = (0.9 * Population at the beginning of year) /100 (Round off)

People allowed to migrate in country = 100,000

Population at the end of year= (Population at the beginning of year) + Total Births + Total Immigrations - Total Deaths.

Population at beginning of year Births Deaths

Immigrations

Population at the end of year 1st Year 3750000 48750 26250 150000 3922500 2nd Year 3922500        50993(round off) 27458(round off) 150000 4096035 3rd Year     4096035 53249 28673 150000 4270611 4th Year 4270611 55518 29894 150000 4446235 5th Year 4446235 57801 31124 150000 4622912 6th Year 4622912 60098 32360 150000 4800650 7th Year 4800650 62409 33605 150000 4979454 8th Year 4979454 64733 34856 150000 5159331 9th Year 5159331 67071 36115 150000 5340287 10th Year 5340287 69424 37382 150000 5522329

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