Certainly! Let's answer each question step-by-step.
### 1. What is the dependent variable?
The dependent variable is the "Number of Developing Clams."
### 2. What is the independent variable?
The independent variable is the "Water Temperature (°C)."
### 3. What trend regarding clam development can you gather from the data?
The trend in the data indicates that the number of developing clams increases as the water temperature rises, reaching a peak at around 30 degrees Celsius. After this peak, the number of developing clams decreases as the temperature continues to increase. Therefore, the best temperature for clam development is around 30 degrees Celsius.
### 4. Approximately how many clams would be developing in 10 degree Celsius water?
To estimate the number of developing clams at 10 degrees Celsius, we can use linear interpolation based on the data points closest to 10 degrees.
Considering the data:
- At 15 degrees Celsius, there are 72 developing clams.
- At 20 degrees Celsius, there are 92 developing clams.
We can calculate the slope (rate of change) between these two points:
[tex]\[ \text{slope} = \frac{92 - 72}{20 - 15} = \frac{20}{5} = 4 \][/tex]
Using the line equation to predict the number of clams at 10 degrees Celsius:
[tex]\[ \text{clams at 10°C} = 72 + 4 \times (10 - 15) \][/tex]
[tex]\[ \text{clams at 10°C} = 72 + 4 \times (-5) \][/tex]
[tex]\[ \text{clams at 10°C} = 72 - 20 \][/tex]
[tex]\[ \text{clams at 10°C} = 52 \][/tex]
Therefore, approximately 52 clams would be developing in 10 degree Celsius water.
