The temperature in a room is changing at a steady rate. If x is the number of minutes since noon, the
temperature was -4° C when x = -3 minutes and the temperature was 6° C when x = -5 minutes. Find the rate
of change in temperature in degrees per minute.
The answer is -5. How do i do this
you want the slope of the line through
(-3,-4) and (-5,6)
That is
10/-2 = -5
Not quite sure why the negative time values. I guess that means minutes before noon.
To find the rate of change in temperature in degrees per minute, you need to determine how much the temperature changes over a certain time interval.
First, let's define the variables:
x - the number of minutes since noon
T(x) - the temperature at time x
We are given that the temperature T(x) is changing at a steady rate. This means that the change in temperature over a given time interval is constant.
Let's take the time interval from x = -3 minutes to x = -5 minutes, which corresponds to a time difference of 2 minutes. Within this interval, the temperature changes from -4°C to 6°C.
Change in temperature = final temperature - initial temperature
Change in temperature = 6°C - (-4°C)
Change in temperature = 10°C
Change in time = final time - initial time
Change in time = -5 minutes - (-3 minutes)
Change in time = -5 minutes + 3 minutes
Change in time = -2 minutes
Now, divide the change in temperature by the change in time to find the rate of change in temperature:
Rate of change in temperature = Change in temperature / Change in time
Rate of change in temperature = 10°C / -2 minutes
Rate of change in temperature = -5°C per minute
Therefore, the rate of change in temperature is -5°C per minute.