Question

Jonah is looking at some information for the obstacle course he 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, 7.25), (2, 7.975), (3, 8.7725), (4, 9.64975) Help Jonah use an explicit formula to find the average time he will need for the 9th obstacle.

Answer 1

Tn=15.55

Explanation:

Jonah is looking at some information for the obstacle course he 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, 7.25), (2, 7.975), (3, 8.7725), (4, 9.64975) Help Jonah use an explicit formula to find the average time he will need for the 9th obstacle.

`T_(n) =ar^(n-1)`

the nth term of a geometric sequence is given by the above equation'

So the explicit formula to find the average time will be by that equation,

we know the time is geometric sequence because the ratio of the 2nd term to the first term is equal to the ratio of the third term to the second term

`T_(n) =ar^(n-1)`

a=first term

n=number of terms

r=common ratio

Tn=nth term of an exponential progression

`T_(n) =ar^(n-1)`

Tn=7.25(1.1)^(9-1)

Tn=7.25*2.14358881

Tn=15.55

for n value of 9 , the time taken to complete the obstacle is 15.55

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Answer 2

(9, 15.5410188725)

Explanation:

The explicit formula for a geometric sequence with first term 7.25 and common ratio 1.1 is ...

y = 7.25·1.1^(x-1)

For x=9, the y-value is ...

y = 7.25·1.1^8 = 15.5410188725 . . . minutes

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Comment on the answer

This time period has a resolution of about 30 nanoseconds, which is completely nonsensical in the context of an obstacle course. It is written in all its decimal glory after the fashion of the numbers given in the problem statement.