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)
The population in 1990 is P 1990 = P 1980 + 100% × P 1980 = 2 P 1980 .
The population in 2000 is P 2000 = P 1990 + 50% × P 1990 = 1.5 P 1990 = 3 P 1980 .
The increase in population from 1980 to 2000 is P 2000 − P 1980 = 3 P 1980 − P 1980 = 2 P 1980 .
The percentage increase from 1980 to 2000 is P 1980 2 P 1980 × 100% = 200% . Therefore, the answer is 200% .
Explanation
Problem Analysis Let's analyze the problem. We are given percentage increases in population over two different time periods and need to find the combined percentage increase over the entire period.
Calculations Let P 1980 be the population in 1980. From 1980 to 1990, the population increased by 100%, so the population in 1990 is: P 1990 = P 1980 + 100% × P 1980 = P 1980 + P 1980 = 2 P 1980 From 1990 to 2000, the population increased by 50%, so the population in 2000 is: P 2000 = P 1990 + 50% × P 1990 = P 1990 + 0.5 P 1990 = 1.5 P 1990 Substituting P 1990 = 2 P 1980 into the equation for P 2000 , we get: P 2000 = 1.5 ( 2 P 1980 ) = 3 P 1980 The increase in population from 1980 to 2000 is: P 2000 − P 1980 = 3 P 1980 − P 1980 = 2 P 1980 The percentage increase from 1980 to 2000 is: P 1980 P 2000 − P 1980 × 100% = P 1980 2 P 1980 × 100% = 2 × 100% = 200% .
Final Answer Therefore, the combined increase for the period 1980-2000 is 200%.
Examples
Understanding percentage increases is crucial in finance. For instance, if you invest $1000 in a stock that increases by 100% in the first year and then by 50% in the second year, your investment would grow to $2000 after the first year and $3000 after the second year. This represents a 200% increase over the initial investment, illustrating the power of compounding returns.
The population of Country X increased by 100% from 1980 to 1990 and by 50% from 1990 to 2000. Overall, the population increased by 200% from 1980 to 2000. Therefore, the answer is 200% .
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