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, 4), (2, 8), (3, 16), (4, 32)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work.
Part C: Use an explicit formula to find the time she will complete the 8th station. Show your work.

Answer 1

At station 5 it will take 128 minutes and at 8th station it will take 512 minutes

a) This data modeling is combination of both as x co-ordinate is a arithmetic sequence while y co-ordinate is a geometric sequence. Hence it is both arithmetic as well as geometric.

b) A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s). For example: The recursive formula of an arithmetic sequence is, an = an-1 + d. The recursive formula of a geometric sequence is, an = an-1r. By observation, the recursive formula becomes

$(x_{n},y_{n}) = (x_{n-1} +1,2y_{n-1})$

Given: (x1=1, y1 =4)

by recursive formula,

(x2,y2) = (1+1,2x1) = (2,8)

(x3,y3) = (3,16)

(x4,y4) = (4,32)

(x5,y5) = (5,64)

Thus at station 5 it will take 128 minutes.

c) By observation the explicit formula is

(xn,yn) = (n,$2^{n+1}$)

Thus (x8,y8) = (8,512)

Thus at 8th station it will take 512 minutes.

Learn more about Sequence and series here :

https://brainly.com/question/14278705

#SPJ1