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)
50 points if you give part a b and c

Answer 1

Answer:

a) geometric

Step-by-step explanation:

a) geometric

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term, but it is not like this, so it is a geometric sequence.

Answer 2

SOLUTION

TO DETERMINE

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?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

EVALUATION

PART : A

Here it is given that 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)

So the time is 3 , 6 , 12 , 24

First term = a = 3

Common Ratio = 2

So the time are in Geometric Progression

Hence the data modeling is a geometric sequence

PART : B

We see that if s is station number and t is time then

Ts=3 x $2^{s-1}$

Which is the required recursive formula to determine the time

Hence the required time she will complete station 5

=t5

=3 x $2^{5-1}$

=3 x 16

= 48

PART : C

The time she will complete station 8

=t8

=3x$2^{8-1}$

=3x$2^{7}$

=384

The time she will complete station 9

=t9

=3x$2^{9-1}$

=3 x 2⁸

=768

Hence the required time she will complete the 9th station

=t₉-t₈

=768-384

=384