To analyze the situation, we begin with the number of trees in the forest five years ago, which was \( f \). Today, the number of trees is represented by \( 1.33f \).
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Increase calculation:
- The increase in the number of trees is: \[ 1.33f - f = 0.33f \]
- To determine the percentage increase: \[ \text{Percentage Increase} = \left(\frac{0.33f}{f}\right) \times 100% = 33% \]
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Equivalent expression:
- The total number of trees today can be expressed as: \[ f + 0.33f = 1.33f \]
Now we can evaluate the options provided in the statements:
A. The number of trees in the forest increased by 133%. An equivalent expression that represents this situation is \( f + 1.33f \).
- False: The increase is 33%, not 133%. The expression is incorrect too; \( f + 1.33f = 2.33f \).
B. The number of trees in the forest decreased by 133%. An equivalent expression that represents this situation is \( f - 1.33f \).
- False: There was an increase, not a decrease.
C. The number of trees in the forest decreased by 33%. An equivalent expression that represents this situation is \( f - 0.33f \).
- False: There was an increase, not a decrease.
D. The number of trees in the forest increased by 33%. An equivalent expression that represents this situation is \( f + 0.33f \).
- True: This accurately reflects the situation.
Thus, the correct answer is D.
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