The country of Growtopia has a real GDP in the previous year of 1,450,000,000 dollars. The current year real GDP was 1,510,000,000 dollars. Based on this information, approximately how long would it take for Growtopia's real GDP to double if it continues to grow at a constant rate? Note, they don't mention the rule of 70 here, but the key is that they ask how long it will take to double if it continues to grow at a constant rate. The first thing we need to know is the growth rate, and then we can use the rule of 70 to estimate how long it would take to double. First, we need to calculate the growth rate using our percentage change formula.

To calculate the growth rate, use the current year GDP of 1,510,000,000 minus the previous year GDP of 1,450,000,000. The formula used is New minus Old divided by Old. Let's calculate it:
√ 1.51 − 1.45 divided by 1.45, which yields a percentage change. Calculating this, 1.51 − 1.45 divided by 1.45, gives us approximately 4.1379%.

It's important to use many decimals to get a precise answer. We typically don't want to round until the last step in any calculation to ensure accuracy. With our growth rate now identified, we can use the rule of 70 to determine how long it would take to double Growtopia's GDP:
√ 70 divided by 4.1379, which results in approximately 16.9192 years.

This calculation shows the importance of precision in the initial steps to ensure the final answer is accurate. With this process, we estimated it would take around 17 years for the GDP of Growtopia to double, assuming a constant growth rate.

Now, try a practice problem to apply what we've discussed.