Based on the model, what will be the mean diameter of the phytoplankton cells that are found 25 kilometers from shore?
Understand the Problem
The question is asking for the mean diameter of phytoplankton cells located 25 kilometers from the shore based on a model that predicts changes in diameter based on distance from the shore. The cells closest to the shore have a mean diameter of 900 micrometers, and the diameter decreases by 50 micrometers for every 5kilometer increase in distance from the shore.
Answer
$650$ micrometers
Answer for screen readers
The mean diameter of the phytoplankton cells that are found 25 kilometers from shore is $650$ micrometers.
Steps to Solve

Identify the initial diameter The mean diameter of the phytoplankton cells closest to the shore (0 kilometers) is given as 900 micrometers.

Determine the distance from shore We need to calculate the mean diameter at a distance of 25 kilometers from the shore.

Calculate the decrease in diameter per kilometer The diameter decreases by 50 micrometers for every 5 kilometers. To find the reduction for 25 kilometers, we first calculate the number of 5kilometer segments in 25 kilometers: $$ \text{Number of segments} = \frac{25 \text{ km}}{5 \text{ km}} = 5 $$

Calculate total decrease in diameter Multiply the decrease per segment by the number of segments: $$ \text{Total decrease} = 50 \text{ micrometers/segment} \times 5 \text{ segments} = 250 \text{ micrometers} $$

Find the mean diameter at 25 kilometers Subtract the total decrease from the initial diameter: $$ \text{Mean diameter at 25 km} = 900 \text{ micrometers}  250 \text{ micrometers} = 650 \text{ micrometers} $$
The mean diameter of the phytoplankton cells that are found 25 kilometers from shore is $650$ micrometers.
More Information
The model highlights how variations in nutrient availability can affect the sizes of phytoplankton, which is crucial for understanding marine ecosystems. Smaller phytoplankton can absorb nutrients more efficiently, which can impact marine food webs.
Tips
One common mistake is neglecting to calculate the number of 5kilometer segments correctly, which can lead to an incorrect total decrease in diameter. Always ensure you divide the total distance by the segment distance correctly.