Question

the data in the table represent the height of an object over time. which model best represents the data? height of an object time (seconds) height (feet) 0 5 1 50 2 70 3 48 4 4 quadratic, because the height increases and then decreases exponential, because the height of the object increases or decreases with a multiplicative rate of change quadratic, because the height of the object increases or decreases with a multiplicative rate of change exponential, because the height increases and then decreases

Explanation:

Step1: Analyze exponential - rate of change

Exponential functions have a multiplicative rate of change. If we check the height values: from $t = 0$ to $t=1$, height changes from $5$ to $50$ (a factor of $10$), from $t = 1$ to $t = 2$, height changes from $50$ to $70$ (a factor of $\frac{70}{50}=1.4$), from $t = 2$ to $t = 3$, height changes from $70$ to $48$ (a factor of $\frac{48}{70}\approx0.69$). The rate - of - change is not multiplicative.

Step2: Analyze quadratic - shape of data

Quadratic functions often have a graph that is a parabola, which can increase and then decrease. Looking at the height values, the height first increases from $t = 0$ to $t = 2$ (from $5$ to $70$) and then decreases from $t = 2$ to $t = 4$ (from $70$ to $4$). This behavior is characteristic of a quadratic function.

Answer:

quadratic, because the height increases and then decreases