A meteorologist recorded the temperatures at two weather stations in Montana. At midnight, the temperature at Station A was -8 degrees Fahrenheit, and it increased at a constant rate of 3 degrees per hour. At midnight, the temperature at Station B was -2 degrees Fahrenheit, and increased at a constant rate of 2 degrees per hour.

Question

What do we know about how the temperature changes over the course of the day at each station?

The temperatures at both stations do not increase at a constant rate.

The temperature increases at a constant rate at both stations.

The temperature at Station A increases at a constant rate, but Station B does not increase at a constant rate.

Answer 1

The correct statement is: The temperature increases at a constant rate at both stations.

At Station A, the temperature starts at -8 degrees Fahrenheit and increases at a rate of 3 degrees per hour. This means that the temperature at Station A can be represented by the equation:

\[ T_A(t) = -8 + 3t \]

where \( T_A(t) \) is the temperature at time \( t \) (in hours after midnight).

At Station B, the temperature starts at -2 degrees Fahrenheit and increases at a rate of 2 degrees per hour. This can be represented by the equation:

\[ T_B(t) = -2 + 2t \]

where \( T_B(t) \) is the temperature at time \( t \) (in hours after midnight).

Both equations show that the temperature at each station increases linearly over time, which indicates a constant rate of change.