From 1980 through 1990, the population of Country X increased by [tex]$100 \%$[/tex]. From 1990 to 2000, the population increased by [tex]$50 \%$[/tex]. What was the combined increase for the period 1980-2000?
(A) [tex]$150 \%$[/tex]
(B) [tex]$166 \frac{2}{3} \%$[/tex]
(C) [tex]$175 \%$[/tex]
(D) [tex]$200 \%$[/tex]
Answer (2)
Assume the initial population in 1980 is P .
Calculate the population in 1990 after a 100% increase: P + 100% × P = 2 P .
Calculate the population in 2000 after a 50% increase: 2 P + 50% × 2 P = 3 P .
Determine the overall percentage increase from 1980 to 2000: P 3 P − P × 100% = 200% . The final answer is 200% .
Explanation
Problem Analysis Let's analyze the problem. We are given percentage increases over two periods and need to find the combined percentage increase over the entire period.
Population in 1990 Let P be the population in 1980. From 1980 to 1990, the population increased by 100% , so the population in 1990 is P + 100% × P = P + P = 2 P .
Population in 2000 From 1990 to 2000, the population increased by 50% , so the population in 2000 is 2 P + 50% × 2 P = 2 P + P = 3 P .
Total Population Increase The total increase in population from 1980 to 2000 is 3 P − P = 2 P .
Percentage Increase Calculation The percentage increase in population from 1980 to 2000 is P 2 P × 100% = 2 × 100% = 200% .
Final Answer Therefore, the combined increase for the period 1980-2000 is 200% .
Examples
Understanding percentage increases is crucial in many real-world scenarios. For example, if you invest money and it grows by a certain percentage each year, you can calculate the total percentage increase over several years to see how much your investment has grown. Similarly, businesses use percentage increases to track sales growth, market share, and other key performance indicators. This concept is also useful in understanding inflation rates and economic growth.
The combined population increase for Country X from 1980 to 2000 is 200%. The calculations show that the population increased from P to 3P throughout this period. Therefore, the answer is 200%.
;
