Problema Solution
The temperature of a pot of water on a stove is being monitored. At the beginning the temperature is 69, after 5 minutes it is 101, and after 9 minutes it is 126.6. Is the temperature rising linearly? Write an equation for the temperature of the water in terms of the number of minutes. What is the temperature of the water when it was placed on the stove? When will the water at sea level begin to boil?
Answer provided by our tutors
The temperature is rising linearly if the slope from time 0 to 5 and 5 to 9 is the same.
Slope(t 0 - 5) = y2-y1/x2-x1 (y is temperature, x is time)
=(101-69)/(5-0) (initial time is 0)
=32/5
=6.4
Slope (t 5 - 9) = y2-y1/x2-x1
=(126.6-101)/(9-5)
=6.4
The slope is the same, therefore the temperature is rising linearly!
The equation is: y = 6.4x + 69
The +69 is the y-intercept, representing the temperature at time 0. The temperature rises at 6.4 degrees per minute.
The temperature of the water is 69 degrees when it is placed on the stove.
Assuming this is celsius (boiling temperature 100 degrees Celsius)
100 = 6.4x + 69
31 = 6.4x
x = 4.84 Minutes
Assuming this is fahrenheit (boiling temperature 212 degrees Fahr)
212 = 6.4x + 69
143 = 6.4x
x = 22.34 Minutes