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Interpret exponential expressions word problems

The expression [tex]5(2)^t[/tex] gives the number of leaves on a plant as a function of the number of weeks since it was planted.

What does 2 represent in this expression?

Choose 1 answer:
A. The plant was planted 2 weeks ago.
B. The number of leaves is multiplied by 2 each week.
C. There were initially 2 leaves on the plant.

Sagot :

GinnyAnsweridn
The given expression is 5(2^n), representing the number of leaves on a plant as a function of the number of weeks, [tex]\( n \)[/tex], since it was planted.

Let's break it down step-by-step to understand its components:

1. The form of the expression is 5 (base number) multiplied by 2 raised to the power of [tex]\( n \)[/tex] (number of weeks).
2. The coefficient 5 indicates the initial number of leaves on the plant.
3. The base number 2 in the exponent indicates the rate at which the number of leaves multiplies every week.

Given this structure, the specific question asks what the number 2 represents in the expression.

Reviewing the options:
- "The plant was planted 2 weeks ago." This option is not correct because there is no direct correlation with planting time in the exponent.
- "The number of leaves is multiplied by 2 each week." This option correctly describes the role of the base number in the exponent: each week, the number of leaves doubles (multiplies by 2).
- "There were initially 2 leaves on the plant." This option is incorrect because the initial number of leaves, indicated by the coefficient, is 5.

Therefore, the correct interpretation is:
The number of leaves is multiplied by 2 each week.
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