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How are levels maintained within an ecosystem? - OCR 21st CenturyScience calculations

Plants compete for light, water, minerals and space. Animals compete for food, mates and territory. Decay is the breakdown of organic matter and is affected by temperature, water and oxygen.

Part of Biology (Single Science)Living together - Food and ecosystems

Science calculations

Rate changes show how quickly something is happening. The rate of change can be calculated using this equation:

We can calculate the rate of change from the results of the experiment on the previous page.

Milk was incubated at three different temperatures and the pH recorded every 24 hours.

Temperature (°C)0 hours24 hours48 hours72 hours
56.56.46.46.0
206.56.15.54.8
356.55.14.84.8
5
0 hours6.5
24 hours6.4
48 hours6.4
72 hours6.0
20
0 hours6.5
24 hours6.1
48 hours5.5
72 hours4.8
35
0 hours6.5
24 hours5.1
48 hours4.8
72 hours4.8

To calculate the rate of change we first need to know the change, or difference, from the previous point for each value. These calculations and answers are shown in the table below.

Temperature (°C)0 hours24 hours48 hours72 hours
5-6.5 - 6.4 = 0.16.4 - 6.4 = 0.06.4 - 6.0 = 0.4
20-6.5 - 6.1 = 0.46.1 - 5.5 = 0.65.5 - 4.8 = 0.7
35-6.5 - 5.1 = 1.45.1 - 4.8 = 0.34.8 - 4.8 = 0.0
5
0 hours-
24 hours6.5 - 6.4 = 0.1
48 hours6.4 - 6.4 = 0.0
72 hours6.4 - 6.0 = 0.4
20
0 hours-
24 hours6.5 - 6.1 = 0.4
48 hours6.1 - 5.5 = 0.6
72 hours5.5 - 4.8 = 0.7
35
0 hours-
24 hours6.5 - 5.1 = 1.4
48 hours5.1 - 4.8 = 0.3
72 hours4.8 - 4.8 = 0.0

Because we started at pH 6.5 at zero hours there is no rate change. Similarly, because the milk did not change from pH 4.8 in the last 24 hours at 35°C there is no rate change here.

We now need to divide each change in value by the change in time (24 hours).

The rate of pH change is measured in ph/hour

Temperature (°C)24 hours48 hours72 hours
50.1 Ă· 24 = 0.10 Ă· 24 = 0.00.4 Ă· 24 = 0.4
200.4 Ă· 24 = 0.40.6 Ă· 24 = 0.60.7 Ă· 24 = 0.7
351.4 Ă· 24 = 1.40.3 Ă· 24 = 0.30 Ă· 24 = 0.0
5
24 hours0.1 Ă· 24 = 0.1
48 hours0 Ă· 24 = 0.0
72 hours0.4 Ă· 24 = 0.4
20
24 hours0.4 Ă· 24 = 0.4
48 hours0.6 Ă· 24 = 0.6
72 hours0.7 Ă· 24 = 0.7
35
24 hours1.4 Ă· 24 = 1.4
48 hours0.3 Ă· 24 = 0.3
72 hours0 Ă· 24 = 0.0

The greatest rate of change is shown in bold above.

Graph showing rates of pH change at different times after incubation Rate of change can also be calculated from graphs
Graph showing rates of pH change at different times after incubation

Rate of change can also be calculated from graphs. Here we use this equation:

The rate of change can be calculated from the above graph by finding the gradient of the trendline, using the equation above

The rate of change can be calculated from the above graph by finding the gradient of the trend line, using the equation above

For example after 0 hours in the above graph, the pH is 6.6; after 50 hours it is 5.4

\(\text{Rate of change} =\frac{vertical~change}{horizontal~change}\)

\(\text{Rate of change} = \frac{5.4 - 6.6~pH~units}{50 - 0~hours}\)

\(\text{Rate of change} = \frac{-1.2~pH~units}{50~hours}\)

\(\text{Rate of change} = -0.024 pH units/hour (to~2~significant~figures)\)

The calculated rate of -0.024 pH units/hour is the mean of the rates shown by the red line in the first graph.

Using the gradient of a graph to find a rate of change is easier than calculating rate when there is a lot of data, or when the data shows a great deal of variability.

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