The capacity of solar power installed in the United States has grown since 2000. The capacity of solar power installed in the United States can be modeled as
m(x) = 15.45(1.46x) megawatts between 2000 and 2008, where x is the number of years since 2000.† (Round your answers to three decimal places.) How much solar power capacity was installed in 2005?

The function \( m(x) = 15.45(1.46^x) \) models the solar power capacity in megawatts installed in the U.S., where \( x \) represents the number of years since 2000.

To find the solar power capacity installed in 2005, calculate the value of \( m(x) \) when \( x = 2005 - 2000 = 5 \).

The function becomes:

\[
m(5) = 15.45(1.46^5)
\]

Now, I'll compute this.The solar power capacity installed in 2005 was approximately 102.493 megawatts.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. How would the solar power capacity change if the growth rate were higher?
2. How much capacity would have been installed in 2008 based on this model?
3. What would the capacity be if the growth rate were 1.3 instead of 1.46?
4. How does the model compare to the actual growth in solar power capacity since 2008?
5. What is the cumulative capacity installed over the entire 2000-2008 period?

**Tip**: Exponential growth models like this one are powerful but may overestimate growth in the long term if external factors limit the expansion.

The capacity of solar power installed in the United States has grown since 2000. The capacity of solar power installed in the United States can be modeled as m(x) = 15.45(1.46^x) megawatts between 2000 and 2008, where x is the number of years since 2000. (Round your answers to three decimal places.) How much solar power capacity was installed in 2005?

Explore the exponential growth model m(x) = 15.45(1.46^x) to calculate the solar power capacity installed in the U.S. between 2000 and 2008. This problem, suitable for Grades 9-12, demonstrates exponential growth in real-world applications like renewable energy. Learn how to compute the capacity for 2005 with step-by-step guidance.

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