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) Required:
a. Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer.
b. Use a recursive formula to determine the time she will complete station. Show your work.
c. Use an explicit formula to find the time she will complete the 8th station. Show your work.

Step-by-step explanation:

Table representing the station number (x-coordinates) and time to complete the task (y-coordinate) is,

x         1           2           3           4

y         4          8          16          32

a). Ratio of second term to the first term of 'y' =

    Ratio of 3rd and 2nd term =

    There is a common ratio 'r' = 2

    Therefore, this data model a geometric sequence.

b). Recursive formula of a geometric sequence is represented by,

    nth term

      Previous term of the nth term

    Therefore, recursive formula for the given data will be,

c). Explicit formula of a geometric sequence is given by,

   Here, a = First term

   r = common ratio

   n = number of term

    nth term

   Explicit formula for the given sequence will be,

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2