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"Let \( v(t) \) be the volume of rain falling onto a flat roof of a house at time \( t \), and \( f(t) \) be the rate at which the rain is collected in a barrel from the roof at time \( t \). What function would be appropriate for the situation?"

This question suggests a problem related to the relationship between the rate of rainfall and the collection of rainwater in a barrel.

### Explanation:
1. **\( v(t) \) represents the total volume of rain falling on the roof over time.**
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Let v(t) be the volume of rain falling onto a flat roof of a house at time t, and f(t) be the rate at which the rain is collected in a barrel from the roof at time t. What function would be appropriate for the situation?

Explore a calculus problem involving the relationship between the volume of rainfall and the rate of collection in a barrel. Understand key concepts such as rate of change, integration, and apply the Fundamental Theorem of Calculus. Suitable for high school students in Grades 11-12.

Math Problem Statement

Solution

Explanation:

$v(t)$ represents the total volume of rain falling on the roof over time.

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