need an expression only to this word problem: An experiment is underway to test the extreme effect of a newly developed liquid. Two hours into the experiment the temperature if the liquid measured to be -17 degrees Celsius. After eight hours of h experiment the temperature of the liquid is -47 degrees Celsius. Assume that the temperature has been changing at constant rate throughout the experiment and will continue to do so.
temp= m*time+k
-17=m*2+k
-47=m*8+k
subtract second equation from first.
30=6m
solve for m, then put it back into either equation, solve for k.
WHATS THE EQUATION FOR THAT PROBLEM
To find the expression that represents the temperature change over time, we need to determine the rate of change of temperature.
We are given the temperature of the liquid at two different times: two hours into the experiment (-17 degrees Celsius) and eight hours into the experiment (-47 degrees Celsius). The temperature change over this period is -47 - (-17) = -30 degrees Celsius.
The time interval between these two measurements is 8 hours - 2 hours = 6 hours.
Now, we can calculate the rate of change per hour by dividing the temperature change by the time interval:
Rate of change = Temperature change / Time interval
Rate of change = -30 degrees Celsius / 6 hours
Rate of change = -5 degrees Celsius per hour
Therefore, the expression that represents the temperature of the liquid over time is:
Temperature = -5t + T0
Where:
- Temperature represents the temperature of the liquid at any given time t.
- t represents the time (in hours) elapsed since the start of the experiment.
- T0 represents the initial temperature of the liquid at t = 0 (the start of the experiment).
In this case, since the temperature at t = 0 is not given, we cannot determine the specific expression for the temperature over time.