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.


A.f(9) = 7.25(1.1)9; f(9) = 17.095

B.f(9) = 1.1(7.25)8; f(9) = 8396469

C.f(9) = 1.1(7.25)9; f(9) = 60874407

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

Answer 1

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

Explanation:

Answer 2

D. y[9]=15.5410

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.