The growth of a tree in Andy's backyard has slowed down as the tree has continued to age. The heights of the tree over the past four years are: 10 feet, 11 feet, 12.1 feet, and 13.31 feet. Write a recursive formula for the height of the tree

9.091(1.1^n)

Step-by-step explanation:

Given the height of a tree for the past 4 years given by the sequence;

10ft, 11ft, 12.1ft, 13.31ft...

We can see that the sequence is in geometric progression since they have a common ratio;

The nth term of a geometric progression is expressed as;

Tn = ar^n-1

a is the first term

r is the common ratio

Given

a = 10

r = 11/10 = 21.1/11 = 13.31/12.1 = 1.1

Substitute into the formula;

Tn = 10(1.1)^{n-1}

Tn = 10(1.1^n)/1.1

Tn = 9.091(1.1^n)

Hence the recursive formula for the height of the tree is expressed as  9.091(1.1^n) where n is the total number of tree.

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40