Questions: The "net up" counter (using technology to count fish passing upstream) at Roe River42 showed that there were 5801 fish in 2006, but that number dropped by 1911 fish in 2013. Compute the percentage change from 2006 to 2013: %.

The "net up" counter (using technology to count fish passing upstream) at Roe River42 showed that there were 5801 fish in 2006, but that number dropped by 1911 fish in 2013. Compute the percentage change from 2006 to 2013: %.

Transcript text: (1 point) The "net up" counter (using technology to count fish passing upstream) at Roe River42 showed that there were 5801 fish in 2006 , but that number dropped by 1911 fish in 2013. Compute the percentage change from 2006 to 2013: \%.

Solution

Solution Steps

To compute the percentage change from 2006 to 2013, we need to:

Calculate the difference in the number of fish between the two years.
Divide this difference by the number of fish in 2006 to find the change relative to the initial value.
Multiply the result by 100 to convert it to a percentage.

Step 1: Initial Values

Let \( \text{fish}_{2006} = 5801 \) be the number of fish in 2006.

Step 2: Calculate Fish Count in 2013

The number of fish in 2013 is given by: \[ \text{fish}_{2013} = \text{fish}_{2006} - 1911 = 5801 - 1911 = 3890 \]

Step 3: Calculate the Difference

The difference in the number of fish from 2006 to 2013 is: \[ \text{difference} = \text{fish}_{2006} - \text{fish}_{2013} = 5801 - 3890 = 1911 \]

Step 4: Calculate Percentage Change

The percentage change from 2006 to 2013 is calculated as: \[ \text{percentage change} = \left( \frac{\text{difference}}{\text{fish}_{2006}} \right) \times 100 = \left( \frac{1911}{5801} \right) \times 100 \approx 32.9426 \]