Math 101: Popalation Growth using the \"Compound Interest\" Formula NAME: 1. Nig
ID: 2799904 • Letter: M
Question
Math 101: Popalation Growth using the "Compound Interest" Formula NAME: 1. Nigeria has a yearly birth rate of 40.2 births per 1000 people and a death rate of 16.7/T000 people. What is the annual growth rate? (a percentage is "per 100") The current population of Nigeria is 135 million people. If we consider this growth to be "compounded yearly". what will be the population ten years from now? What will the population be in ten years if we consider the growth as "compounded daily? 2. Who will add more people to their country in the next ten years? (Use compounded yearly for these) Show how many people will be added to each country: Country United States 2008 population How many people added after 10 years Growth rate 301,000,000 1,322,000,000 1,130,000,000 109,000,000 0.92% 0.58% 1.40% 1.17% China India Mexico 3. In 1963, the world population was 3.2 billion and the yearly growth rate was about 2.3%. this rate what wlthe planet look Ike in 20507 20 18 16 14 Year Population billions) 1963 3.2 1970 1980 1990 2000 2010 2020 2030 2040 2050 1970 1980 19 2000ues010 20 230 204 2oso yeaExplanation / Answer
1) Net population increase per year = (40.2 - 16.7) = 23.5 per 1000 people
Annual growth rate, g = 2.35%
Compounded yearly, Population in 10 years = 135 x (1 + 2.35%)^10 = $170.3 million
Compounded daily, Population in 10 years = 135 x (1 + 2.35%/365)^3650 = $170.8 million
2) No. of people added can be calculated using following equation
Addition = P x [(1 + g)^n - 1], where P - Current Population, g - growth rate, n - no. of years
For US, No. of people added = 301,000,000 x [ (1 + 0.92%)^10 - 1] = 28,867,033
For China, No. of people added = 1,322,000,000 x [(1 + 0.58%)^10 - 1] = 78,708,513
For India, No. of people added = 1,130,000,000 x [(1 + 1.4%)^10 - 1] = 168,547,957
For Mexico, No. of people added = 109,000,000 x [(1 + 1.17%)^10 - 1] = 13,445,830