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)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Source&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;StylesFormatFontSize&nbsp;&nbsp;&nbsp;&nbsp;

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Aurora is planning to participate in an event at her school&#039;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)&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;Source&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;StylesFormatFontSize&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;

alenahelenash · Accepted Answer

Part A: To determine if the data models an arithmetic sequence or a geometric sequence, we need to examine the pattern between the y-coordinates (time) for each station.The given data points are: (1, 4), (2, 8), (3, 16), (4, 32).If we observe the pattern, we can see that the time doubles for each consecutive station. Starting from the first station, the time is 4 minutes, then it doubles to 8 minutes for the second station, then 16 minutes for the third station, and finally 32 minutes for the fourth station.This pattern indicates that the data is modeling a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio.Part B: To determine the time Aurora will complete station 5 using a recursive formula, we need to find the common ratio in the geometric sequence.From the given data, we can see that the common ratio between consecutive terms is 2. Therefore, the recursive formula for the time she will complete station 5 can be expressed as:an=an−1×rwhere an represents the time for station n, an−1 is the time for the previous station, and r is the common ratio.Using the values from the given data, we have:a1=4 (time for the first station)r=2 (common ratio)To find a5, we can apply the recursive formula:a5=a4×ra5=32×2=64Therefore, Aurora will complete station 5 in 64 minutes.Part C: To find the time Aurora will complete the 8th station using an explicit formula, we need to find a general formula that relates the station number to the time.In a geometric sequence, the explicit formula is given by:an=a1×r(n−1)where an represents the time for station n, a1 is the time for the first station, r is the common ratio, and n is the station number.Using the given data, we have:a1=4 (time for the first station)r=2 (common ratio)To find a8, we can substitute the values into the explicit formula:a8=4×2(8−1)a8=4×27=4×128=512Therefore, Aurora will complete the 8th station in 512 minutes.The solutions are represented as:Part A: The given data models a geometric sequence.Part B: a5=a4×r=32×2=64Part C a8:=a1×r(8−1)=4×27=512

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Aurora is planning to participate in an event

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