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Difficulty: MediumPercents and Percent Change

In 2018, a forestry service recorded 400400 pine trees in a specific section of a nature reserve. Due to a reforestation initiative, the number of pine trees in this section increased by 15%15\% from 2018 to 2021. From 2021 to 2024, the number of pine trees increased by 20%20\% of the number of pine trees in 2021. What was the number of pine trees in this section of the reserve in 2024?

  1. A
    480
  2. B
    540
  3. C
    542
  4. 552Answer

Answer

The correct number of pine trees in the reserve in 2024 is 552.
To find the number of pine trees in 2024, first calculate the population in 2021. A 15%15\% increase on the initial 400400 trees results in 400×1.15=460400 \times 1.15 = 460 trees. Next, find the population in 2024 by applying a 20%20\% increase to the 2021 population of 460460 trees, which yields 460×1.20=552460 \times 1.20 = 552 trees.

Step-by-Step Solution

1
Calculate the number of pine trees in 2021 after the 15%15\% increase.
400×(1+0.15)=460400 \times (1 + 0.15) = 460 trees
The initial number of trees in 2018 was 400400, and it increased by 15%15\%, so we multiply 400400 by 1.151.15.
2
Calculate the number of pine trees in 2024 after the 20%20\% increase.
460×(1+0.20)=552460 \times (1 + 0.20) = 552 trees
The percentage increase of 20%20\% from 2021 to 2024 is based on the 2021 tree population of 460460, so we multiply 460460 by 1.201.20.

Key Concept

Calculating successive percentage increases by applying each percentage change to the correct sequential baseline value.

Alternative Method

Alternatively, you can compute the final value in a single expression by multiplying the initial value by both growth factors: 400×1.15×1.20=552400 \times 1.15 \times 1.20 = 552.
Estimated Time:1m 30s
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Topics

Percents and Percent Change

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