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 asks for the mean diameter of phytoplankton cells found at a distance of 25 kilometers from shore based on a model that indicates a change of 50 micrometers for every 5-kilometer increase in distance from the shore, starting from a mean diameter of 900 micrometers.
Answer
The mean diameter of the phytoplankton cells found 25 kilometers from shore is $650$ micrometers.
Answer for screen readers
The mean diameter of the phytoplankton cells found 25 kilometers from shore is $650$ micrometers.
Steps to Solve
-
Identify the initial mean diameter
The mean diameter of phytoplankton cells closest to shore is given as 900 micrometers. -
Determine the distance from shore
The distance stated in the problem is 25 kilometers from shore. -
Calculate the number of 5-kilometer intervals
To find how many 5-kilometer intervals fit into 25 kilometers, divide:
$$ \text{Number of intervals} = \frac{25 \text{ km}}{5 \text{ km}} = 5 $$ -
Calculate the total change in diameter
The change in mean diameter for each interval is 50 micrometers. Therefore, for 5 intervals:
$$ \text{Total change} = 5 \times 50 \text{ micrometers} = 250 \text{ micrometers} $$ -
Find the new mean diameter
Subtract the total change from the initial mean diameter:
$$ \text{New mean diameter} = 900 \text{ micrometers} - 250 \text{ micrometers} = 650 \text{ micrometers} $$
The mean diameter of the phytoplankton cells found 25 kilometers from shore is $650$ micrometers.
More Information
This answer indicates that as phytoplankton cells are located further from the shore, their mean diameter decreases due to reduced nutrient availability.
Tips
- Failing to correctly calculate the number of intervals by not dividing properly.
- Subtracting incorrectly; ensure that you are deducting the total change from the initial diameter.
