at the start of the day, the temperature in antarctica was $-16^{\circ}\text{c}$. as the day went on, the temperature rose at a constant rate of $1.5^{\circ}\text{c}$ per hour. what was the temperature after 7 hours?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Modeling", "Signed Numbers" ], "new_concepts": [], "current_concepts": [ "Linear Modeling", "Signed Numbers", "Rate of Change" ] } ## Define the linear model parameters $$ \begin{aligned} T_0 &= -16^\circ\text{C} \ r &= 1.5^\circ\text{C/hour} \ t &= 7\text{ hours} \end{aligned} $$ ## Calculate the total temperature change $$ \Delta T = r \cdot t = 1.5 \cdot 7 = 10.5^\circ\text{C} $$ ## Determine the final temperature $$ T_f = T_0 + \Delta T = -16 + 10.5 = -5.5^\circ\text{C} $$ $-5.5^\circ\text{C}$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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Explanation:

Define the linear model parameters

Calculate the total temperature change

Determine the final temperature

Answer: