A robot on Mars records the temperature every Mars day. A summary series, showing every one hundredth Mars day, is shown in the table below.
Number of Mars days ( n )
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
Temp. ( ∘C )
-43
-15
-5
-21
-59
-79
-68
-50
-27
-8
-15
-70
-78
-68
(a) Find the maximum and minimum temperatures recorded by the robot.
(b) Use the data to estimate the length of a Mars year.
(c) Without using technology, find a sine model for the temperature T in terms of the number of Mars days n.
(d) Draw a scatter diagram of the data and sketch the graph of your model on the same set of axes.
(e) Check your answer to c using technology. How well does your model fit?