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Zorluk: OrtaPercent Change and Interest

A boutique dairy farm produced 4,0004,000 liters of organic milk in 2021. The annual milk production increased by 15%15\% from 2021 to 2022, decreased by 10%10\% from 2022 to 2023, and then increased by 20%20\% from 2023 to 2024. How many liters of organic milk did the farm produce in 2024?

Cevap: 4968 liters

Cevap

The farm produced 4,968 liters of organic milk in 2024.
To calculate the final quantity after sequential percent changes, multiply the starting amount by the multiplier for each period. The net expression is 4,000×1.15×0.90×1.204,000 \times 1.15 \times 0.90 \times 1.20. Stepwise, 4,000×1.15=4,6004,000 \times 1.15 = 4,600, then 4,600×0.90=4,1404,600 \times 0.90 = 4,140, and finally 4,140×1.20=4,9684,140 \times 1.20 = 4,968 liters.

Adım Adım Çözüm

1
Calculate milk production in 2022 after a 15% increase.
4,000×1.15=4,6004,000 \times 1.15 = 4,600 liters
An increase of 15% corresponds to multiplying the initial base value by 1+0.15=1.151 + 0.15 = 1.15.
2
Calculate milk production in 2023 after a 10% decrease.
4,600×0.90=4,1404,600 \times 0.90 = 4,140 liters
A decrease of 10% corresponds to multiplying the new base value of 4,600 by 1−0.10=0.901 - 0.10 = 0.90.
3
Calculate milk production in 2024 after a 20% increase.
4,140×1.20=4,9684,140 \times 1.20 = 4,968 liters
An increase of 20% corresponds to multiplying the current base value of 4,140 by 1+0.20=1.201 + 0.20 = 1.20.

Anahtar Kavram

Successive Percent Change
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Percent Change and Interest

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