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The height of a tree follows a geometric progression in the first month the tree grew 40 inches in the second month it grows 36 inches the third month it grows by 32.4 inches determine its height in feet after six years?

Respuesta :

asuwafohjames

The height of the tree after 6 years is 33.32 feet.

What is height?

This is the vertical distance between two points.

To calculate the height of the tree after six years, we use the formula below.

Formula:

Sₙ = a(1-rⁿ)/(1-r)...................... Equation 1

Where:

  • Sₙ = Height of the tree after six years.
  • a = Height of the tree in the first month
  • r = common ratio of the tree
  • n = number of terms in months.

From the question,

Given:

  • a = 40 inches
  • r = 36/40 = 0.9
  • n = 6 years = (6×12) = 72 months

Substitute these values into equation 1

  • Sₙ = 40(1-0.9⁷²)/(1-0.9)
  • Sₙ = 40(1-0.000507)/0.1
  • Sₙ = 40(0.999493)/0.1
  • Sₙ = 399.7972 inches
  • Sₙ = 33.32 feet

Hence, The height of the tree after 6 years is 33.32 feet.
Learn more about height here : https://brainly.com/question/1739912

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