Question

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

Answer 1

9.091(1.1^n)

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.