Question

6. A hot air balloon rises from the ground. Does the height of the balloon vary directly with the time it has been in the air? How do you know? Time (minutes) 5 7 10 15 Height (feet) 70 98 140 210

Answer 1

yes, it vary directly with the time, because:

`\begin{gathered} \text{let:} \\ h=\text{height} \\ t=\text{time} \\ h(t)=kt \\ \text{Where:} \\ k=\text{constant of proportionality} \end{gathered}`

For t = 5 , h = 70

so:

`\begin{gathered} 70=k\cdot5 \\ k=(70)/(5) \\ k=14 \end{gathered}`

If:

`\begin{gathered} t=7\colon \\ h(7)=14\cdot7=98 \\ t=10\colon \\ h(10)=14\cdot10=140 \\ t=15\colon \\ h(15)=14\cdot15=210 \end{gathered}`

Since there is a constant of direct proportionality for each of the values, the function varies directly