To determine how long it would take for the real GDP of Growtopia to double, we first need to calculate the growth rate using the percentage change formula. The formula for percentage change is:

Percentage Change = \(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\)

In this case, the previous year's real GDP is 1,450,000,000 and the current year's real GDP is 1,510,000,000. Plugging these values into the formula gives us:

Percentage Change = \(\frac{1,510,000,000 - 1,450,000,000}{1,450,000,000} \times 100\)

Calculating this, we find:

Percentage Change = \(\frac{60,000,000}{1,450,000,000} \times 100 \approx 4.1379\%\)

Next, to find out how long it will take for the GDP to double at this growth rate, we can use the Rule of 70. This rule states that the approximate number of years required to double an investment can be found by dividing 70 by the annual growth rate:

Years to Double = \(\frac{70}{\text{Growth Rate}}\)

Substituting the growth rate we calculated:

Years to Double = \(\frac{70}{4.1379} \approx 16.9192\) years

Rounding this to the nearest whole number, it would take approximately 17 years for Growtopia's real GDP to double if it continues to grow at the same rate. This example illustrates the importance of precise calculations and the potential impact of rounding at different stages of the calculation process.