Question

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, 3), (2, 6), (3, 12), (4, 24)

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 9th station. Show your work. (4 points)

Answer 1

Step-by-step explanation:

A. this is a geometric sequence.

according to y-coordinates =>

3, 6, 12, 24

have a T1 = 3 and ratio = 6/3 = 2

B. the formula = Tn = r. T(n-1)

T5 = 2. T4

= 2. 24 = 48 minutes

C. the formula : Tn = T1 . r^(n-1)

T9 = 3. 2^(9-1)

= 3. 2^8

= 3. 256

= 768 munutes