The growth rate of GDP from year 1 to year 2 for the considered hypothetical economy is given by: Option D: 25%
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Growth rate (in percentage) of GDP is the percent of previous years GDP the next year GDP is.
For first year, GDP = $6 billion
For second year, GDP = $7.5 billion
So the difference is of 1.5 billion dollar increment in GDP.
Thus, the rate of growth of GDP from first year to second year is $1.5 billion per year.
Now we need to find out how much 1.5 billion dollars increment is in comparison to the first year GDP (so as to know how much percent is increased).
Let we have: 1.5 billion is P% of 6 billion
Then, we get:
[tex]\dfrac{6000000000}{100} \times P = {1500000000}\\\\60000000 \times P = 1500000000\\\\\text{Dividing both the sides by 60000000, we get:}\\\\P = \dfrac{1500000000}{60000000} = 25 \: \rm (in \: percent)[/tex]
So second year's GPD is 25% incremented compared to the first year's GDP.
Thus, the growth rate of GDP from year 1 to year 2 for the considered hypothetical economy is given by: Option D: 25%
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