Suppose you want to double 10,000 in 3 years What annual growth rate for an exponential model using the 70 rule

The "Rule of 70" is a simple way to estimate the time it takes for an investment or quantity to double, given a constant annual growth rate. The formula is:

\[
\text{Doubling Time} \approx \frac{70}{\text{Annual Growth Rate (\%)}}
\]

In your case, you want the amount to double in **3 years**. We can rearrange the formula to solve for the annual growth rate:

\[
\text{Annual Growth Rate (\%)} \approx \frac{70}{\text{Doubling Time}}
\]

Substitute 3 years for the doubling time:

\[
\text{Annual Growth Rate (\%)} \approx \frac{70}{3} = 23.33\%
\]

So, the required annual growth rate is approximately **23.33%** per year.

### Do you need further details or have any questions?

Here are five related questions to consider:

1. How does the Rule of 70 compare with the Rule of 72 for estimating growth?
2. What if the doubling time was extended to 5 years—what would be the new growth rate?
3. How does the exponential growth formula compare to the Rule of 70 in accuracy?
4. What if you had to halve your amount in 3 years—what decay rate would you need?
5. How does compound interest factor into exponential growth models?

**Tip:** The Rule of 70 works best for growth rates under 20%; for very high rates, the Rule of 72 may give more accurate results.

Suppose you want to double 10,000 in 3 years. What annual growth rate for an exponential model using the 70 rule?

Find out how to calculate the annual growth rate to double an investment in 3 years using the Rule of 70. Learn the key concepts of exponential growth, and use the simple formula: Annual Growth Rate ≈ 70 / Doubling Time. Perfect for high school students.

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