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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.

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 :

mhanifa

Answer:

  • A) Exponential, B) f(x) = 2*2ˣ, C) 12

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Part A

The y-coordinates form a GP with the common ratio of 2:

  • 4, 8, 16, 32

It indicates the function is not linear but exponential.

Part B

The relation between x- and y-coordinates is:

  • x = 1, y = 4 or y = 2*2¹
  • x = 2, y = 8 or y = 2*2²
  • x = 3, y = 16 or y = 2*2³
  • x = 4, y = 32 or y = 2*2⁴

So the function is:

  • f(x) = 2*2ˣ

Part C

The average rate of change between station 2 and station 4 is:

  • [f(4) - f(2)] / (4 - 2) =
  • (32 - 8)/2 =
  • 24/2 =
  • 12

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