Question

An object is dropped from a building and allowed to freefall to the ground. The height of the object over time is shown in the table. (For reference: h(t) = 144 – 16t2) Time (seconds) Height (feet) 0 144 1 128 2 80 3 0 Which statement describes the rate of change of the height of the object over time? The rate of change is constant with the object dropping 1 foot every second. The rate of change is constant with the object dropping 144 feet every second. The rate of change decreases over time. The object is 128 feet above ground after one second, but 80 feet after two seconds. The rate of change increases over time. The object drops 16 feet in the first second, but 80 feet in the last second.

Answer 1

the correct answer will be D

Answer 2

Answer:

The rate of change increases over time.

The object drops 16 feet in the first second, but 80 feet in the last second.

Step-by-step explanation:

We are given the table,

Time (seconds)  (x)                         Height (feet) (y)

        0                                                144    

        1                                                 128

        2                                                 80

        3                                                  0

Now, Rate of change is equal to the ratio of change in height and change in time.

That is, Rate of change = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

So, we find the rate for the different time intervals.

A.. Rate in [0,1] = $\frac{128-144}{1-0}$ = -16 feet per second

B. Rate in [1,2] = $\frac{80-128}{2-1}$ = -48 feet per second

C. Rate in [2,3] = $\frac{0-80}{3-2}$ = -80 feet per second

So, we see that,

The rate is increasing in magnitude over time and in the 1st second, the rate is 16 feet and in the last second, the rate is 80 feet.

Hence, the statements describing rate of change are,

The rate of change increases over time.

The object drops 16 feet in the first second, but 80 feet in the last second.