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PLEASE HELP ASAP!!! WILL GIVE BRAINLIEST
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. (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)

Respuesta :

mhanifa

Given pairs of coordinates:

  • (1, 2), (2, 4), (3, 8), (4, 16)

We can see the x-coordinates come in sequence from 1 through 4 and the y-coordinates are:

  • 2, 4, 8, 16

Part A

We can show the y-coordinates as:

  • 2 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴

This is an exponential function.

Part B

The function is the general form of the y-coordinates given in relation with x-coordinates:

  • f(x) = 2ˣ

Part C

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

  • (f(4) - f(2)) / (4 - 2) = (16 - 4)/(4 - 2) = 12/2 = 6

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