The remaining credit after 71 minutes is $21.48
To solve this, we can calculate the equation of the linear function that represents the remaining credit
x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation
34 min and $25.92 => (34,25.92)
53 min and 23.64 => (53,23.64)
the formula to calculate the slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}=\frac{23.64-25.92}{53-34}=-0.12[/tex]
now we know the slope, we can get the line euqation
[tex]y=m(x-x_1)+y_1\Rightarrow\text{ y=-0.12(x-34)+25.92=-0.12x+30}[/tex]
Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.
for x=71 min:
[tex]y=-0.12(71)+30=-8.52+30=21.48[/tex]
theremaining credit is $21.48.
