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 $\textcolor{b l u e}{25}$#### Explanation: Let $t = \text{Time}$and $c = \text{Cost}$$t \textcolor{w h i t e}{888888} c$$3 \textcolor{w h i t e}{888888} 75$$4 \textcolor{w h i t e}{888888} 100$$5 \textcolor{w h i t e}{888888} 125$$6 \textcolor{w h i t e}{888888} 150$The rate of change is the change in $c$divided by the change in $t$$\frac{{c}_{2} - {c}_{1}}{{t}_{2} - {t}_{1}}$Starting at the top of the table: $\frac{100 - 75}{4 - 3} = 25$$\frac{125 - 100}{5 - 4} = 25$$\frac{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 $\left(3 , 75\right)$This point is from the table: $\left({c}_{2} - {c}_{1}\right) = m \left({t}_{2} - {t}_{1}\right)$$c - 75 = 25 \left(t - 3\right)$$c = 25 t\$

This is it's graph:

You can see that this follows the table above,