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

2 Answers
Jun 26, 2018

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) :}#

Jun 26, 2018

#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:

enter image source here

You can see that this follows the table above,