Question

researchers propose a model to explain variation in phytoplankton cell sizes in a marine environment. they base their model on the idea that smaller cells absorb nutrients more efficiently. the researchers predict that the mean diameter of phytoplankton cells will change by 50 micrometers for every 5 - kilometer increase in distance from the shore because of a gradual decrease in nutrient availability. to test their model, the researchers determine that the phytoplankton cells found closest to shore have a mean diameter of 900 micrometers. based on the model, what will be the mean diameter of the phytoplankton cells that are found 25 kilometers from shore? a) 650 micrometers b) 875 micrometers c) 925 micrometers d) 1150 micrometers

Explanation:

Step1: Determine the distance increment

The distance from shore is 25 kilometers. Since the decrease is 50 micrometers for every 5 - kilometer increase in distance from shore, we first find out how many 5 - kilometer intervals are in 25 kilometers. The number of 5 - kilometer intervals $n=\frac{25}{5}=5$.

Step2: Calculate the total decrease in diameter

Since the decrease in diameter per 5 - kilometer interval is 50 micrometers, and there are 5 such intervals, the total decrease in diameter $\Delta d = 50\times5=250$ micrometers.

Step3: Calculate the mean diameter

The initial mean diameter is 900 micrometers. The new mean diameter $d = 900-\Delta d$. Substituting the value of $\Delta d = 250$ micrometers, we get $d=900 - 250=650$ micrometers.

Answer:

A. 650 micrometers