This problem requires us to determine the uniform annual rate at which industrial power consumption increased. We are given that the consumption doubled over a specific period of 10 years.

Understanding Industrial Power Growth

When a quantity, such as industrial power consumption, grows at a constant annual rate, it follows the principle of compound growth. This means that the increase each year is calculated on the accumulated amount from the previous year, not just on the initial amount. The standard formula for compound growth is:

\[ A = P(1 + r)^n \]

• \(A\) represents the final amount of industrial power consumption after \(n\) years.
• \(P\) represents the initial amount of industrial power consumption.
• \(r\) represents the annual rate of increase, expressed as a decimal.
• \(n\) represents the number of years over which the growth occurs.

Identifying Key Information for Power Calculation

Let's extract the crucial information provided in the question to solve for the annual rate of increase:

• Time Period: The industrial power consumption increased from 2000-2001 to 2010-2011.
• Number of Years (\(n\)): The total duration for this increase is \(2010 - 2000 = 10\) years.
• Growth Factor: The problem states that industrial power consumption "doubled". This implies that the final consumption \(A\) is exactly twice the initial consumption \(P\). Mathematically, we can write this as \(A = 2P\).

Calculating the Annual Rate of Increase

Now, we will substitute these known values into our compound growth formula:

\[ A = P(1 + r)^n \]

Since \(A = 2P\) and \(n = 10\), our equation becomes:

\[ 2P = P(1 + r)^{10} \]

To simplify, we can divide both sides of the equation by \(P\), assuming \(P\) is not zero:

\[ 2 = (1 + r)^{10} \]

To find the value of \((1 + r)\), we need to take the 10th root of both sides of the equation:

\[ 1 + r = 2^{(1/10)} \]

Next, we calculate the numerical value of \(2^{(1/10)}\):

\[ 2^{(1/10)} \approx 1.071773 \]

Now, we can solve for \(r\):

\[ r = 1.071773 - 1 \]

\[ r \approx 0.071773 \]

To express this annual rate as a percentage, we multiply it by 100:

\[ \text{Annual Rate of Increase (in percent)} = r \times 100\% \]

\[ \text{Annual Rate of Increase} \approx 0.071773 \times 100\% \]

\[ \text{Annual Rate of Increase} \approx 7.1773\% \]

Rounding this value to one decimal place, which is common for percentage rates, we get:

\[ \text{Annual Rate of Increase} \approx 7.2\% \]

Conclusion on Power Consumption Rate

Based on the calculations, the uniform annual rate of increase in industrial power consumption, which doubled over a period of 10 years, is approximately 7.2%.