If latex: \{a_i: i\in i\} is a collection of open subsets of latex: \mathbb{r} , then latex: \cup_{i\in i}a_i is open in latex: \mathbb{r}

(can this be proved without the concept of the open ball from topology)

Data for the height of a model rocket launch in the air over time are shown in the table. darryl predicted that the height of the rocket at 8 seconds would be about 93 meters. did darryl make a good prediction? yes, the data are best modeled by a quadratic function. the value of the function at 8 seconds is about 93 meters. yes, the data are best modeled by a linear function. the first differences are constant, so about 93 meters at 8 seconds is reasonable. no, the data are exponential. a better prediction is 150 meters. no, the data are best modeled by a cubic function. a better prediction is 100 meters.