Assuming that the polynomial relationship between the period and the distance is linear. The graphical representation of the values given in the table can be used to derived the polynomial relationship.
If the values of the periods is plotted on the x-axis against the values of the distance on the y-axis.
The graph of the period against the distance is as shown below:
From the graph above the relationship between the period and the distance is
Where y is the distance and x is the period
(b) Given that the distance is 11,483 thousands of kilometers, the value of the period can be calculated by substituing for y in the relationship gotten above
According to the model, the period is approximately 117days
(c) If the actual period is 252 days, compare to the value of the period calculated using the polynomial model
The value from the modelled relationship is 117 days and the actual period is 252 days. It can be seen that the period from the model is less than the actual period with 137 days.
It can be concluded that the period from the modelled is not close to the actual value
The possible source of errors could be because the relationship modelled the points given in the table. The points plotted were scattered as shown in the graph.
ANSWER SUMMARY
(a) The polynomial model of the relationship between period and distance for Jupiter moon is y = 95.5817x + 313.741
(b) If the distance is 11483 days, using the model, the number of period is approximately 117 days
(c) Comapring the model value and the actual period is not close. The possible source of errors could be because the linear graph of the points plotted are scattered