# Jonah is looking at some information for the obstacle course he is interested in completing. The x-coordinate is the number of

###### Question:

## Answers

f(8) = 1.1(6.25)8; f(8) = 2561137

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

Step-by-step explanation:

Need One? Look at Their's ^^^

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

Step-by-step explanation:

* Lets explain how to solve the problem

∵ The x-coordinate is the number of the obstacle

∵ The y-coordinate is the average time to complete the obstacle

∵ The order pairs of function are (1 , 8.25) , (2 , 9.075) , (3 , 9.9825) ,

(4 , 10.98075)

- From these order pairs

# The time to finish the 1st obstacle is 8.25 minutes

# The time to finish the 2nd obstacle is 9.075 minutes

# The time to finish the 3rd obstacle is 9.9825 minutes

# The time to finish the 4th obstacle is 10.98075 minutes

∵ 2nd ÷ 1st = 9.075/8.25 = 1.1

∵ 3rd ÷ 2nd = 9.9825/9.075 = 1.1

∵ 4th ÷ 3rd = 10.98075/9.9825 = 1.1

∴ There is a constant ratio 1.1 between each 2 consecutive terms

∴ The order pairs formed a geometric series

- Any term in the geometric series Un = a r^(n - 1) , where a is the 1st

term in the series , r is the constant ratio and n is the position of the

term in the series

∵ a = 8.25 ⇒ the time of the first obstacle

∵ r = 1.1

- Sheila wants to find the average time she will need for the 8th

obstacle

∴ n = 8

∵ The explicit formula is f(x) = a r^(n - 1)

∴ f(8) = 8.25 (1.1)^(8 - 1)

∴ f(8) = 8.25(1.1)^7

∴ f(8) = 16.076916 ≅ 16.077

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

(9, 15.5410188725)

Step-by-step 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

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.

f(8) = 6.25(1.1)^7 ; f(8) = 12.179

Step-by-step explanation: (I got it right on the test)

(1, 6.25), (2, 6.875), (3, 7.5625), (4, 8.31875)

r= 1.1

f(1) = 6.25 / starting number

1. Since it is multiplying each number by 1.1 it is using the Geometric Explicit Formula:

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

f(8) = 6.25 x 1.1 ^(8-1)

f(8) = 6.25 x 1.1 ^7

f(8) = 6.25 x 1.9487171

f(8) = 12.179

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

Step-by-step explanation:

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

D. y[9]=15.5410

Step-by-step explanation:

Let's find the answer by using the following observation:

Notice that the y-value differences between consecutives obstacles are:

(y-value from obstacule 2) - (y-value from obstacule 1)= 7.975 - 7.25 = 0.725

which is equal to:

(y-value from obstacule 1) / 10 = 7.25 / 10 = 0.725

So, an equation can be written as follows:

y[i+1]=y[i]+y[i]/10 let's find the other values:

y[2]=7.25+(7.25/10)= 7.975

y[3]=7.975+(7.975/10)= 8.7725

y[4]=8.7725+(8.7725/10)= 9.64975

Notice that we obtained the same y-values using the formula as the ones reported. So using the same formulas we can calculate:

y[9]=15.5410

In conclusion, the general equation is y[i+1]=y[i]+y[i]/10 with a starting point (1, 7.25) and y[9]=15.5410. So the answer is D.

D.) f(9) = 7.25(1.1)8; f(9) = 15.541

Step-by-step explanation:

D

Step-by-step explanation:

I think

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

Step-by-step 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 = [tex]\frac{9.075}{8.25}[/tex] = 1.1

The explicit formula for a geometric sequence is:

[tex]f(n)=f(1)(r)^{n-1}[/tex]

Using the values, we get:

[tex]f(n)=8.25(1.1)^{n-1}[/tex]

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

[tex]f(8)=8.25(1.1)^{8-1}\\\\ f(8)=8.25(1.1)^{7} \\\\ f(8)=16.077[/tex]

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