the gross domestic product (GDP) of a certain country is growing at a constant rate. In 2009 the GDP was 125 billion dollars , and in 2011 it was 155 billion dollars. At what percentage rate will the GDP grow in 2014?
Find the rate per year. That is take the difference between 155 and 125 and divide it by the number of years between 2009 and 2011. Then multiply this yearly rate by the number of years between 2011 and 2014.
Dear Tom;
This is not the final solution yet...
Sincerely, Ms Pi
To determine the percentage rate at which the GDP will grow in 2014, we need to calculate the average annual growth rate between 2009 and 2011 and apply that rate to project the GDP for 2014.
Step 1: Calculate the average annual growth rate
To find the average annual growth rate, we will use the formula:
Average annual growth rate = ((GDP for 2011 / GDP for 2009) ^ (1 / number of years)) - 1
In this case, the GDP for 2011 is $155 billion, and the GDP for 2009 is $125 billion. The number of years between 2009 and 2011 is 2.
Average annual growth rate = (($155 billion / $125 billion) ^ (1 / 2)) - 1
Step 2: Calculate the GDP for 2014
To project the GDP for 2014, we will use the formula:
GDP for 2014 = GDP for 2011 * ((1 + average annual growth rate) ^ number of years)
In this case, the number of years between 2011 and 2014 is 3.
GDP for 2014 = $155 billion * ((1 + average annual growth rate) ^ 3)
Now, let's calculate the values.
Average annual growth rate = (($155 billion / $125 billion) ^ (1 / 2)) - 1
Average annual growth rate ≈ 0.0989 or 9.89%
GDP for 2014 = $155 billion * ((1 + 0.0989) ^ 3)
GDP for 2014 ≈ $195.453 billion
Therefore, the projected GDP for 2014 is approximately $195.453 billion, and the growth rate from 2011 to 2014 is approximately 9.89%.