the data in the table represent the height of an object over time. which model best represents the data…

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

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

Answer

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