Question

Can u help me find the rate of change is constant in each table? Find the rate of change. Explain what the rate of change means for the situation? Time (days) Cost ($) 3 75 4 100 5 125 6 150

Answer 1

The rate of change is `$25` per day.
This means that the cost increases by `$25` from one day to the next

Explanation:

`{: (ul("Day"),ul("Cost $"),,), (3,75,,), (4,100,"change from day 3 to day 4",=$100-$75=$25),(5,125,"change from day 4 to day 5",=$125-$100=$25),(6,150,"change from day 5 to day 6",=$150-$125=$25) :}`

Answer 2

`color(blue)(25)`

Explanation:

Let `t="Time"` and `c= "Cost"`

`tcolor(white)(888888)c`

`3color(white)(888888)75`
`4color(white)(888888)100`
`5color(white)(888888)125`
`6color(white)(888888)150`

The rate of change is the change in `c` divided by the change in `t`

`(c_2-c_1)/(t_2-t_1)`

Starting at the top of the table:

`(100-75)/(4-3)=25`

`(125-100)/(5-4)=25`

`(150-125)/(6-5)=25`

This suggest that the function is linear ( a straight line )

The rate of change in this case `25`, is really stating that for every unit of time in this case a day, the cost changes by `25` dollars. Notice that `25` is positive. This means the cost will be rising as time increases.

The function could be found if necessary in the following way.

Using point slope form of a line, with `m=25` and point `(3,75)`

This point is from the table:

`(c_2-c_1)=m(t_2-t_1)`

`c-75=25(t-3)`

`c=25t`

This is it's graph:

You can see that this follows the table above,