Question

Sheila is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of the obstacle, while the y-coordinate is the average time to complete the obstacle, measured in minutes.

(1, 8.25), (2, 9.075), (3, 9.9825), (4, 10.98075)

Help Sheila use an explicit formula to find the average time she will need for the 8th obstacle.

f(8) = 8.25(1.1)^8; f(8) = 17.685
f(8) = 8.25(1.1)^7; f(8) = 16.077
f(8) = 1.1(8.25)^7; f(8) = 2861345
f(8) = 1.1(8.25)^8; f(8) = 23606102

Answer 1

B // f(8) = 8.25(1.1)^7; f(8) = 16.077

Explanation:

I'm Pretty Sure She's Got It ^^^

Answer 2

f(8) = 8.25(1.1)^7; f(8) = 16.077

Explanation:

In order to calculate the explicit formula we need to look at the y coordinates. All the options list the formula of a Geometric Sequence, so we will find which sequence defines the given coordinates:

The sequence is:

8.25, 9.075, 9.9825, 10.98075

f(1) = First term of the Sequence = 8.25

r = Common Ratio = Ratio of two consecutive terms =
`(9.075)/(8.25)` = 1.1

The explicit formula for a geometric sequence is:

`f(n)=f(1)(r)^(n-1)`

Using the values, we get:

`f(n)=8.25(1.1)^(n-1)`

For 8th term, we have to replace n by 8:

`f(8)=8.25(1.1)^(8-1)\\\\ f(8)=8.25(1.1)^(7) \\\\ f(8)=16.077`

So, second option gives the correct answer: f(8) = 8.25(1.1)^7; f(8) = 16.077