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, 2), (2, 4), (3, 8), (4, 16)

Part A: Is this data modeling a linear function or an exponential function? Explain your answer.

Part B: Write a function to represent the data. Show your work.

Part C: Determine the average rate of change between station 2 and station 4. Show your work.

Answer 1

She will need a time of 1024 units to complete the 10th station.

Explanation:

A. As the quotient between consecutive terms is the same, the data is a geometric sequence.

B. The recursive formula is:

C. She will need a time of 1024 units to complete the 10th station.

In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.

If the quotient between consecutive terms is the same, the sequence is geometric.

Item a:

When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.