Question

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

• A quadratic function has a parabolic graph. A parabola has a maximum or minimum point. In the given data, the height first increases (from \(t = 0\) to \(t=1\) and \(t = 1\) to \(t = 2\)) and then decreases (from \(t=2\) to \(t = 3\) and \(t=3\) to \(t = 4\)).
• An exponential function has the form \(y = a\cdot b^{x}\) (\(b>0,b

eq1\)). If \(b > 1\), it is an increasing exponential function (\(y\) increases as \(x\) increases) and if \(0 < b<1\), it is a decreasing exponential function (\(y\) decreases as \(x\) increases). An exponential function does not have a maximum - minimum behavior (it either always increases or always decreases or has a horizontal asymptote but no local maximum/minimum in the domain of real numbers for a simple exponential function \(y=a\cdot b^{x}\)).

Answer:

quadratic, because the height increases and then decreases