A company bought a plant for production. The manufacturing capacity of the plant reduces by 12% ever

Question

A company bought a plant for production. The manufacturing capacity of the plant reduces by 12% every year. If the plant was able to produce 874 kg of raw materials in the first year. How many kg of raw materials would the plant be able to produce at the end of the 15th years?

Answer 1

A company bought a plant for production. The manufacturing capacity of the plant reduces by 12% every year. If the plant was able to produce 874 kg of raw materials in the first year. How many kg of raw materials would the plant be able to produce at the end of the 15th years?

165.88 kg
145.97 kg
128.46 kg ✓
113.04 kg

Explanation

Losing 12% each year means the plant keeps 100% − 12% = 88% of the previous year’s output. Keeping 88% is the same as multiplying by 0.88. So this is a geometric (repeated multiplying) problem, not a subtraction one.

Starting output is 874 kg, and by the end of the 15th year the 12% drop has happened 15 times. So output = 874 × 0.88¹⁵.

Work out 0.88¹⁵ step by step: 0.88² = 0.7744, 0.88⁴ = 0.5997, 0.88⁸ = 0.3596, and 0.88¹⁵ = 0.88⁸ × 0.88⁴ × 0.88² × 0.88 ≈ 0.14697.

Now multiply: 874 × 0.14697 ≈ 128.46 kg. So the plant produces about 128.46 kg. (If you only apply the drop 14 times you get about 145.97 kg, which is why that value appears as a trap.)

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