Question

Compare the doubling times found with the approximate and exact doubling time formulas. Then use the exact doubling time formula to answer the given question. A nation of 100 million people is growing at a rate of 10% per year. What will its population be in 5 years?

Answer 1

To calculate the population after 5 years for a nation growing at 10% per year, use the compound growth formula. The population will grow from 100 million to approximately 161 million in 5 years.

Step-by-step explanation:

Using the exact doubling time formula, we can calculate the future population of a nation growing at a specific rate. The formula to find the doubling time is T = 70 / r, where T is the doubling time in years and r is the growth rate percentage. For a nation growing at 10% per year, the doubling time would be T = 70 / 10, which is 7 years. However, if we want to calculate the population after a certain period, such as 5 years in this case, we use the compound growth formula P = P0 × (1 + r)n, where P is the final population, P0 is the initial population, r is the growth rate (expressed as a decimal), and n is the number of periods (years).

For the nation with an initial population of 100 million people and a growth rate of 10% per year, the population after 5 years, P, would be calculated as follows:

P = 100,000,000 × (1 + 0.10)5
P = 100,000,000 × 1.105
P = 100,000,000 × 1.61051
P = 161,051,000

Therefore, the population of the nation in 5 years would be approximately 161 million people.