Please help its important 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. (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 8th station. Show your work. (4 points)

Part A

The sequence is geometric because the y values are doubling each time

4*2 = 8

8*2 = 16

16*2 = 32

The common ratio is r = 2.

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Part B

The recursive rule here would be

The first line says that "the first term is 4"

The second line says "the nth term is found by multiplying 2 by the previous (n-1) term". In other words, double any term to get the next term.

The fourth term is 32 which doubles to 64 and that's the fifth term. So the point (5,64) is on this exponential curve.

She takes 64 minutes to complete station 5

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Part C

We see that a = 4 is the first term and r = 2 is the common ratio.

The explicit nth term formula is a(r)^(n-1) which becomes 4(2)^(n-1)

Plugging in the value n = 8 leads to

4(2)^(n-1)

4(2)^(8-1)

4(2)^7

4(128)

512

You can use the method shown in part B to keep doubling each term until you arrive at the 8th term. This is one way to confirm the answer.

your answer would be 12