Question

1. the table shows the amount of chlorophyll for each trophic class.

trophic status

chlorophyll level (parts per billion)	trophic class	biological productivity
2.6–20	mesotrophic	intermediate
20–56	eutrophic	high
56–155	hypereutrophic	severe

a. the chlorophyll levels from the samples taken are 5.7, 12.3, 17.1, 20.1, and 23.1 parts per billion. what trophic class is indicated by the mean chlorophyll level?
b. give an example of 5 sample chlorophyll levels such that the mean chlorophyll level would classify the lake as eutrophic.

Explanation:

Part (a)

Step 1: Calculate the mean

To find the mean, we sum up all the values and divide by the number of values. The values are \(5.7\), \(12.3\), \(17.1\), \(20.1\), and \(23.1\). The sum is \(5.7 + 12.3 + 17.1 + 20.1 + 23.1 = 78.3\). There are 5 values, so the mean is \(\frac{78.3}{5}=15.66\) parts per billion.

Step 2: Determine the trophic class

Now we check which range \(15.66\) falls into. The ranges are: \(0 - 2.6\) (Oligotrophic), \(2.6 - 20\) (Mesotrophic), \(20 - 56\) (Eutrophic), \(56 - 155\) (Hypereutrophic). Since \(2.6<15.66<20\), it falls into the Mesotrophic range.

For a lake to be classified as Eutrophic, the mean chlorophyll level must be in the range \(20 - 56\) parts per billion. Let's choose 5 values whose mean is in this range. Let's pick values: \(20\), \(25\), \(30\), \(35\), \(40\). The sum is \(20 + 25 + 30 + 35 + 40 = 150\). The mean is \(\frac{150}{5}=30\), which is in the \(20 - 56\) range (Eutrophic range). (Note: There are many possible sets of 5 values, this is just one example.)

Answer:

The trophic class indicated by the mean chlorophyll level is Mesotrophic.

Part (b)