Final answer:
The initial temperature was 40°C and decreased at a rate of 0.5°C per minute. The temperature function is T(t) = -0.5t + 40. By graphing this function, we'll see a straight line depicting the drop in temperature over time.
Step-by-step explanation:
To tackle this problem, we should first find out the initial temperature before Quinn fell asleep. Given that the temperature decreased by 0.5 Celsius degrees per minute for 60 minutes, and ended up at 10 degrees Celsius, we can add this temperature drop to the final temperature to find the initial temperature. That would be 10C + (0.5C/min * 60 min) = 40C. Therefore, the room's initial temperature when Quinn fell asleep was 40 degrees Celsius.
The function that models this situation is a linear function. We can write it in slope-intercept form, which is y = mx + b, where y is the dependent variable (temperature), m is the slope (rate of change of temperature, −0.5°C/min), x is the independent variable (time in minutes), and b is the y-intercept (initial temperature, 40°C).
So, our function becomes: T(t) = -0.5t + 40, where T is temperature and t is time in minutes.
The graph of this function will show a straight line starting from 40°C at time 0 and decreases (-0.5°C/min) as time increases. Choose several points to plot on the graph (like t=0, t=20, and t=60) and connect them to form a line, you'll clearly see how room's temperature changes over time.
Learn more about Graphing a linear function