Answer:
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
