Question

The temperature of a liquid is decreasing at a constant rate. After two minutes of cooling it was 178 degrees and after 5 minutes of cooling it was at 154 degrees. At what temperature did the liquid start cooling. Show how you arrived at your answer

Answer 1

Answer:

Step-by-step explanation:

If the liquid is cooling at a constant rate, then the equation for this is linear.  We can use the info given to find the linear equation for this situation.  We have 2 points: (2, 178) and (5, 154), where the x coordinate represents the time in minutes, and y represents the temperature.  We use these values in the slope formula:

$m=\frac{154-178}{5-2}=-\frac{24}{3}=-8$

Now we will use one of the points to finish writing the equation.  I chose (2, 178), but it doesn't matter which one you choose; they will both give you the same equation in the end.

y - 178 = -8(x - 2) and

y - 178 = -8x + 16 so

y = -8x + 196

If we are looking for the temp when the liquid starting cooling, then we are looking for the temp at time 0, or when x = 0 (sincce x is our time).

y = -8(0) + 196 so

y = 196

That's the temp of the liquid before it started any cooling.