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, 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)

Answer 1

For part A consider sequence of y-values: 4, 8, 16, 32
Are the differences between the terms same or the ratios?

For part B, if its AP, recursive formula is:
\[t _{n}= t_{n-1} + d\]
and if its a GP, recursive formula is:
\[t _{n}= t_{n-1} * r\]
Find the value of \[t_{5}\]
Depending on the result of part A, you will get an explicit formula:
\[t_{n} = t_{1}+(n-1)d\] or
\[t_{n} = t_{1}*r ^{n-1}\]
Find the value of \[t_{8}\]