Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 2), (2, 4), (3, 8), (4, 16)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)

Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)

Part C: Use an explicit formula to find the time she will complete the 10th station. Show your work.

In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.
If the quotient between consecutive terms is the same, the sequence is geometric.

Item a:

When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.

Item b:

The recursive formula for a geometric sequence with common ratio [tex]q[/tex] and first term [tex]a_1[/tex] is given by:

[tex]f(n) = f(n-1)q^{n-1}, f(1) = a_1[/tex]

Hence, since [tex]a_1 = 2, q = 1[/tex]

[tex]f(n) = f(n-1)2^{n-1}, f(1) = 2[/tex]

Item c:

The explicit formula for a geometric sequence with common ratio [tex]q[/tex] and first term [tex]a_1[/tex] is given by:

[tex]a_n = a_1q^{n-1}[/tex]

Hence, in this question:

[tex]a_n = 2(2)^{n-1} = 2^{1 + n - 1} = 2^n[/tex]

For the 10th station:

[tex]a_n = 2^10 = 1024[/tex]

She will need a time of 1024 units to complete the 10th station.

A similar problem is given at https://brainly.com/question/25403784