Question

the data in the table represent the height of an object over time.

height of an object
\

$$\begin{array}{|c|c|} \\hline \\text{time (seconds)} & \\text{height (feet)} \\\\ \\hline 0 & 5 \\\\ \\hline 1 & 50 \\\\ \\hline 2 & 70 \\\\ \\hline 3 & 48 \\\\ \\hline 4 & 4 \\\\ \\hline \\end{array}$$

which model best represents the data?

• quadratic, because the height of the object increases or decreases with a multiplicative rate of change
• quadratic, because the height increases and then decreases
• exponential, because the height of the object increases or decreases with a multiplicative rate of change
• exponential, because the height increases and then decreases

Explanation:

Analyze the trend in the data table

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The height values increase from \(5\) to \(70\) and then decrease back down to \(4\).

Evaluate the model types and justifications

• Quadratic models represent symmetric parabolic motion (such as projectile motion) where values increase to a maximum and then decrease.
• Exponential models represent continuous growth or decay with a multiplicative rate of change, which do not increase and then decrease.
• Therefore, the data is best represented by a quadratic model because the height increases and then decreases.

Answer:

• quadratic, because the height of the object increases or decreases with a multiplicative rate of change
• quadratic, because the height increases and then decreases (Correct answer)
• exponential, because the height of the object increases or decreases with a multiplicative rate of change
• exponential, because the height increases and then decreases