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 . (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 day 2 and day 4. Show your work (4 points )

Answer 1

Explanation:

A

it is an exponential function.

for a linear function the charge rate would have to be constant between any pair of data points.

the change rate is

( f ( interval end ) - f ( interval begin ) ) /

( interval end - interval begin )

between (1, 2) and (2, 4) we have a charge rate of

(4 - 2) / (2 - 1) = 2

between e.g. (3, 8) and (4, 16) we have a charge rate of

(16 - 8) / (4 - 3) = 8

the change rate is therefore not constant, and it is not a linear function.

B

we see

x1 = 1, y1 = 2

x2 = x1 + 1, y2 = y1×2

x3 = x2 + 1, y3 = y2×2

we get the impression that

xn = xn-1 + 1 = x1 + (n - 1)

yn = yn-1 × 2 = y1 × 2^n

so, while going linearly along the x-axis, y increases by the powers of 2.

the function is then

f(x) = 2^x

C

the change rate between station 2 and 4 (NOT day 2 and 4) is

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