A tree is at present 9 feet tall. If every year it grows 1/9 th of its height, what will be the height of the tree after three years?
12 feet
12.34 feet
13 feet
13.10 feet
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2021
– The growth each year is 1/9th of the height at the beginning of that year. This is a compound growth pattern.
– After 1 year, height H₁ = H₀ + (1/9)H₀ = H₀(1 + 1/9) = H₀(10/9).
– After 2 years, height H₂ = H₁ + (1/9)H₁ = H₁(1 + 1/9) = H₁(10/9) = H₀(10/9)(10/9) = H₀(10/9)².
– After 3 years, height H₃ = H₂ + (1/9)H₂ = H₂(1 + 1/9) = H₂(10/9) = H₀(10/9)³.
– Substitute the initial height H₀ = 9 feet:
– H₃ = 9 * (10/9)³ = 9 * (1000 / 729).
– H₃ = 9000 / 729.
– Simplify the fraction by dividing numerator and denominator by 9:
– H₃ = 1000 / 81.
– Calculate the decimal value: 1000 ÷ 81 ≈ 12.34567…
– Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.