In today’s society radioactivity has found numerous applications. Some of the applications include energy production through nuclear reactors, in diagnosis and therapy, and most importantly in the study of animals and plants. This paper entails a report on a research performed by scientists about the rate of decay of a radioactive substance. The paper will display the results obtained by the researchers, plot a scatter plot to check the relationship between weight and time, use the graph utility to come up with an exponential model. Then the exponential model will be graphed in a scatter diagram. The constant found in the model obtained will be interpreted. Also, the half-life of the radioactive substance will be determined and the remaining mass.
Results and interpretation
The following table displays the data collected by the researchers.
| Month | Weight |
| 0 | 1000 |
| 6 | 749.8 |
| 12 | 562.14 |
| 18 | 421.5 |
| 24 | 316 |
| 30 | 236.93 |
| 36 | 177.64 |
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A scatter diagram was drawn from the collected data and the graph obtained was as displayed below
It was observed that there was a negative relationship between weight and Time (months). As time increased the weight of the radioactive material decreased.
The general form of the exponential function was given as
Since the two variables time and weight had a negative relationship, the exponential function became;
The exponential function was graphed using the graphing utility and the following output was obtained;
The half-life of the radioactive material was calculated as follows;
Therefore, the half-life of the radioactive material was determined to be 6 months.
The amount of radioactive material remaining after 30 months was determined by substituting it to the exponential function as follows;
The time when the radioactive material will have the mass of 40 grams was determined as follows;
40 grams = 0.392 Newton
When substituted to the exponential equation yielded;
From the above analysis, it will be easier for the scientist to use the exponential function to predict the weight of the radioactive material remaining than reading direct from the graph. This is because of the convenience and accuracy involved when using the model. It will also enable scientists to give accurate prediction about the remaining mass or time.
References
John, C. (1979). Fluorographic detection of radioactivity in polyacrylamide gols with the water-soluble fluor, sodum salicylate. Analytical biochemistry , 132-135.
L'Annunziata. (2012). Handbook of radoactivity analysis. Academic press .
