Question

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.
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.