Question

READ THE QUESTIONS PROPERLY

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 a linear function or an exponential function? Explain your answer. (2 points)

Part B: Write a function to represent the data. Show your work. (4 points)

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

Answer 1

The correct answers are:A. The data modelling given in the question is Geometric Sequence.B. The time taken by Aurora to complete station 5 is 48 minutes.C. The time taken by her to complete the 9th station is 768 minutes.

Explanation:

A. The data modelling is Geometric Sequence due to the presence of common ratio between each term.

Common ratio is the constant value we get, when we divide one value by the previous one and it is present in Geometric Sequences.

6/3 = 2

12/6 = 2

24/12 = 2

The Common Ratio is 2.

B. Recursive formula can be used by knowing the initial term and common ratio.

Initial Term : Time taken to complete first station = 3 minutes.

Common Ratio: The ratio obtained above = 2

The Recursive Formula for the Geometric Sequence is, an=r.an-1

To find the time taken to reach 5th station, we need to find a5,

a1=3

a2=3*2=6

a3=6*2=12

a4=12*2=24

a5=2*a4

a5=2*24

a5=48

Therefore, the time take by Aurora to complete station 5 is 48 minutes.

C. The Explicit Formula for the Geometric Sequence is:

an=a1*rn-1

Here, a=3, r=2, n=9.

a9=3*29-1

a9=3*28

a9=3*256

a9=768

Hence, it will take Aurora 768 minutes to complete station 9.