Question

Determine the function that represents the following tables. Time (seconds) 1, 4, 7, 10, 13, the Distance (miles) 5 20 35 50 65.

Answer 1

the function is d= f(t)

when t1= 1 , d1= 5

when t2= 4, d2= 20

`\text{rate od change = }(d_2-d_1)/(t_2-t_1)`
`\text{rate of change = }(20-5)/(4-1)=\text{ }(15)/(3)=\text{ 5}`
`\begin{gathered} ifd_{2\text{ }}=20,d_{3\text{ }}=35,t_{2\text{ }}=4,t_{3\text{ }}=7 \\ \text{rate of change = }(d_3-d_2)/(t_3-t_2)\text{ = }(35-20)/(7-4)=\text{ }(15)/(3)=\text{ 5} \end{gathered}`

Thus if d is a function of t

and the rate of change is constant

then d = 5t is the function