Question

maryanne throws a ball off the top of a building. the table shows the height of the ball in feet, (f(t)), at (t) seconds.

\

$$\begin{tabular}{|c|c|c|c|c|c|} \\hline (t) & 0 & 1 & 2 & 3 & 4 \\\\ \\hline (f(t)) & 64 & 96 & 96 & 64 & 0 \\\\ \\hline \\end{tabular}$$

what type of function is represented?

• exponential
• quadratic
• linear
• logarithmic

Explanation:

Calculate first differences of the function values

$$
LATEXBLOCK0
$$

Calculate second differences of the function values

$$
LATEXBLOCK1
$$

(Note: The physical motion of a thrown ball under gravity is modeled by a quadratic function \(f(t) = -16t^2 + v_0t + h_0\). Testing this model with \(f(t) = -16t^2 + 48t + 64\) yields: \(f(0)=64\), \(f(1)=96\), \(f(2)=96\), \(f(3)=64\), \(f(4)=0\), which perfectly matches the table.)

Identify the function type

$$ \text{Function Type} = \text{quadratic} $$

Answer:

• exponential
• quadratic (Correct answer)
• linear
• logarithmic