Question

The population of City X increased from 2 million in the year 2000 to 2.5 million in 2015 and the gross domestic product of the city in 2000 was 3/8 less than that in 2015. What was the approximate percent change, rounded to the nearest integer if required, in the per capita gross domestic product of the city from 2000 to 2015?

A 22% decrease
B 22% increase
C 28% increase
D 53% increase
E 113% increase

Answer 1

To find the percent change in per capita GDP of City X from 2000 to 2015, we calculate the per capita GDP for both years, considering the population and total GDP changes, resulting in a 28% increase.

Step-by-step explanation:

To calculate the approximate percent change in the per capita gross domestic product (GDP) of City X from 2000 to 2015, we need to take into account both the change in population and the change in total GDP.

First, since the GDP in 2015 was only 3/8 less than that in 2000, we can write this as a fraction: 1 - 3/8 = 5/8. This means the GDP in 2000 was 5/8 of the GDP in 2015. If we let G represent the GDP in 2015, then the GDP in 2000 was (5/8)G.

Next, we calculate the per capita GDP for each year. The per capita GDP in 2000 is (5/8)G / 2 million and in 2015 it's G / 2.5 million.

To compare the two, we divide the per capita GDP in 2015 by the per capita GDP in 2000 and subtract 1:

• (G / 2.5 million) / ((5/8)G / 2 million) - 1
• (8/5) * (2 million / 2.5 million) - 1
• (8/5) * (4/5) - 1
• (32/25) - 1
• 1.28 - 1
• 0.28

This result of 0.28 means a 28% increase in per capita GDP from 2000 to 2015. So, the correct answer is C, a 28% increase.

Answer 2

The answer is 22% decrease. (option A)

Step-by-step explanation:

Given that,

2015 population = 2.5 million

2000 population = 2 million

Let GDP (gross domestic product) for the year 2015 = X

then, GDP for the year 2000 = 5/8 X (i.e 3/8 less than that of 2015)

and the per capita GDP for 2015 = 2500000 / X

Also, the per capita GDP for 2000 = 2000000 / (5X /8)

= 3200000 / X

Comparing the per capita GDP of 2015 to that of 2000, there is a decrease from 2000 to 2015.

decrease = year 2000 per capita GDP - year 2015 per capita GDP

= 3200000 / X - 2000000 / X

= 700000 / X

The percentage decrease can be calculated as

percentage decrease = decrease *100 / year 2000 per capita GDP

= (700000 / X) *100 / (3200000/X)

= 21.875

= 22% decrease