Question

The volumes of a water balloon and an air balloon after they are punctured are represented by the

following tables:
Air balloon
Time (seconds) Volume (cubic centimeters)
0
95
3
69
6
50
9
37
12
27
Water balloon
Time (seconds) Volume (cubic centimeters)
0
30
3
15.8
6
7.8
9
4
12
2.1
Determine whether the data described in the tables is best modeled by a linear function or an
exponential function.

Answer 1

Air ballon = exponetal function / water ballon = exponetal function

Explanation:

khan told me :)

Answer 2

Both air balloon and water balloon data are best modeled by an exponential function.

Explanation:

Air balloon

Time (seconds) Volume (cubic centimeters)

0 95

3 69

6 50

9 37

12 27

The relation Volume variation/time is constant for lines, In this case, this value change from point to point, as can be seen next.

(69 - 95)/3 = -8.67

(50 - 69)/3 = -6.33

(37 - 50)/3 = -4.33

(27 - 37)/3 = -3.33

Water balloon

Time (seconds) Volume (cubic centimeters)

0 30

3 15.8

6 7.8

9 4

12 2

(30 - 15.8)/-3 = -4.73

(15.8 - 7.8)/-3 = -2.67

(7.8 - 4)/-3 = -1.27

(4 - 2)/-3 = -0.67

In this case, the relation Volume variation/time also change from point to point.

Then, both air balloon and water balloon data are best modeled by an exponential function.