An experiment is underway to test the effect of extreme temperatures on a newly developed liquid. Two hours into the experiment the temperature of the liquid measured to be -17 degrees celsius. After eight hours of the experiment the temperature of the liquid is -47 degrees celsius. Assume that the temperature has been changing at a constant rate throughout the experiment and will continue to do so. Write and expression for this problem.
went down 30 degrees in six hours
T = - (30/6) t + b = -5 t + b
-17 = -5 (2) + b
b = -7
so
T = -5 t - 7
check at 8 hours
T = -5(8) -7
T = -40 - 7
T = -47, yes, good
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To write an expression for this problem, let's assume that the temperature of the liquid is changing linearly over time. We'll call the initial temperature at time t=0 as T₀ and the rate of change as r (in degrees Celsius per hour).
The expression for the temperature of the liquid at time t can be written as:
T(t) = T₀ + r * t
Given that two hours into the experiment the temperature is -17 degrees Celsius, we can substitute these values into the expression:
-17 = T₀ + r * 2
After eight hours into the experiment, the temperature is -47 degrees Celsius, so we can substitute these values as well:
-47 = T₀ + r * 8
Now we have a system of two equations with two unknowns (T₀ and r). We can solve this system of equations to find the values of T₀ and r.
To write an expression for this problem, we need to determine the rate at which the temperature is changing.
We can start by calculating the change in temperature over the period of six hours (from 2 hours to 8 hours):
Change in temperature = Final temperature - Initial temperature
Change in temperature = -47°C - (-17°C)
Change in temperature = -47°C + 17°C
Change in temperature = -30°C
Now, we know that the temperature change is -30°C over a period of 6 hours. To find the rate at which the temperature is changing per hour, we can divide the change in temperature by the number of hours:
Rate of temperature change per hour = Change in temperature / Number of hours
Rate of temperature change per hour = -30°C / 6 hours
Rate of temperature change per hour = -5°C/hour
Finally, we can write the expression for the temperature as a function of time (t):
Temperature (t) = Initial temperature + (Rate of temperature change per hour) * t
Substituting the given values into the expression:
Temperature (t) = -17°C + (-5°C/hour) * t
Thus, the expression for this problem is:
Temperature (t) = -17°C - 5t, where t is the number of hours since the start of the experiment.