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. linear function exponential function air balloon water balloon

Explanation:

Step1: Check air balloon linearity

Calculate volume differences:
$95-69=26$, $69-50=19$, $50-37=13$, $37-27=10$

Step2: Check air balloon exponentiality

Calculate volume ratios:
$\frac{69}{95}\approx0.726$, $\frac{50}{69}\approx0.725$, $\frac{37}{50}=0.74$, $\frac{27}{37}\approx0.730$

Step3: Check water balloon linearity

Calculate volume differences:
$30-15.8=14.2$, $15.8-7.8=8$, $7.8-4=3.8$, $4-2.1=1.9$

Step4: Check water balloon exponentiality

Calculate volume ratios:
$\frac{15.8}{30}\approx0.527$, $\frac{7.8}{15.8}\approx0.494$, $\frac{4}{7.8}\approx0.513$, $\frac{2.1}{4}=0.525$

Answer:

Air balloon: Linear function
Water balloon: Exponential function