a weather station at the top of a mountain reports that the temperature is currently $0^\circ\text{c}$ and has been falling at a constant rate of $3.5^\circ\text{c}$ per hour. what will the temperature be at the top of the mountain in 5 hours?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Rate of Change", "Linear Modeling" ], "current_concepts": [ "Rate of Change", "Linear Modeling", "Signed Numbers" ] } ## Identify the given values and rate of change $$ \begin{aligned} T_0 &= 0^\circ\text{C} \ r &= -3.5^\circ\text{C/hour} \ t &= 5\text{ hours} \end{aligned} $$ ## Calculate the total change in temperature $$ \Delta T = r \cdot t = -3.5 \cdot 5 = -17.5^\circ\text{C} $$ ## Determine the final temperature $$ T_f = T_0 + \Delta T = 0 + (-17.5) = -17.5^\circ\text{C} $$ $-17.5^\circ\text{C}$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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Question

Explanation:

Identify the given values and rate of change

Calculate the total change in temperature

Determine the final temperature

Answer: