[50 points, with all parts]
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, 4), (2, 8), (3, 16), (4, 32)

part a: is this data modeling an arithmetic sequence or a geometric sequence? explain your answer.

part b: use a recursive formula to determine the time she will complete station 5. show your work.

part c: use an explicit formula to find the time she will complete the 8th station. show your work.

A. It is a geometric sequence.

B.  She will complete station 5 , 64 minutes or 1 hour and 4 minutes after starting.

C. The time she will complete the 8th station is given by,  8 hours and 32 minutes  after starting.

Step-by-step explanation:

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

The co-ordinates are given as following,

x       y

1        4

2       8

3       16

4       32

Hence, it is given as,

Y = minutes(1)

A. So, it is a geometric sequence.

B. The time required by her to complete station 5 is given by,

   Y =    minutes

      =    minutes

      = 64  minutes

Hence, she will complete station 5 , 64 minutes or 1 hour and 4 minutes after starting.

C. The time she will complete the 8th station is given by,

    Y =  minutes

        =  512 minutes

        =    hours

        =   hours

        = 8 hours 32 minutes  (after starting)

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