The temperature of an object in a experiment is T(t) = 60(1/3)^t + 10, where T is the temperature in degrees C and t is time in seconds.
What is the domain and range of this situation?
The important term to consider is
60(1/3)^t, which has a domain of R (all real) and a range of (0,+∞).
Therefore
dom T(t) = R
ran T(t) = (10,∞)
To determine the domain and range of the situation, we need to understand the meaning of the variables and any restrictions they may have.
In this case, "T" represents the temperature in degrees Celsius, and "t" represents time in seconds.
Domain refers to the set of all possible input values for a function, so in this case, it represents the possible values for "t." We need to identify any restrictions or limits on the time.
In this situation, since time is measured in seconds, it is reasonable to assume that the time cannot be negative, as negative time does not make physical sense. Therefore, the domain of this situation would be all non-negative real numbers: [0, ∞).
Range, on the other hand, refers to the set of possible output values for a function, which represents the possible values for "T." We need to determine any limits or constraints on the temperature.
Looking at the given equation, it is clear that the temperature is a function of the expression (1/3)^t. Since any positive number raised to any real power is always positive, we can conclude that the expression (1/3)^t will always be positive as long as t is a real number.
Therefore, the range of this situation would be all positive real numbers greater than the constant term in the equation, which is 10. In other words, the range would be (10, ∞).