Question

write a formula for a linear function that models the situation. state what the input variable represents and the domain of the function. a stone is dropped from a water tower and its velocity increases at a rate of 32 feet per second². the stone hits the ground with a velocity of 256 feet per second. write the formula for v(t). v(t) = 32t what does the input variable represent? ∘ velocity ∘ distance ∘ time ∘ acceleration

Explanation:

For the formula \( v(t) = 32t \) and the input variable question:

The function \( v(t) \) models the velocity of a dropped stone over time. In the context of a falling object (under gravity, with acceleration due to gravity here being 32 ft/s²), the input variable \( t \) in the function \( v(t) \) represents the time elapsed (in seconds, likely) since the stone was dropped. The options given are velocity, distance, time, or acceleration. Velocity is the output (\( v(t) \)), distance would be related to a position function, acceleration is the rate of change of velocity (here, the slope 32 is the acceleration, 32 ft/s²). So the input variable \( t \) represents time.

Answer:

time (the option corresponding to "time" among the choices: velocity, distance, time, acceleration)