Mathematics: 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 an arithmetic sequence or a geometric sequence?

Your answer is three out of the people in your school....

Aurora is planning to participate in an event at

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19.06.2020

Part A: The data modeled is a geometric sequence.

Part B: Aurora will complete station 5 in 32 minutes.

Part C: Aurora will complete station 10 in 1024 minutes.

Step-by-step explanation:

Part A: To find the sequence of the model, we need to find the common ratio.

The data is $\{2,4,8,16\}$ . The common ratio of a geometric series can be found by dividing the second term by first term.

$\begin{aligned}\frac{a_{n}}{a_{n-1}} &=r \\\frac{4}{2} &=r \\2 &=r\end{aligned}$

Thus, the model is a geometric sequence.

Part B: The recursive formula is $a_{n}=r \cdot a_{n-1}$

Now, to find at what time she will complete station 5, let us substitute n=5, we get,

$\begin{aligned}a_{n} &=r \cdot a_{n-1} \\a_{5} &=r \cdot a_{4} \\&=2(16) \\a_{5} &=32\end{aligned}$

Thus, Aurora will complete station 5 in 32 minutes.

Part C: The explicit formula is $a_{n}=a \times r^{n-1}$

To find the time she will complete the 10th station, we shall substitute n=10, we get,

$\begin{aligned}a_{n} &=a \cdot r^{n-1} \\a_{10} &=2 \cdot(2)^{9} \\&=2(512) \\&=1024\end{aligned}$

Thus, Aurora will complete station 10 in 1024 minutes.

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