A)
In order to find the function for the cost C, we can use the slope-intercept form of a linear equation:
[tex]C=mx+b[/tex]Where m is the slope and b is the y-intercept.
To calculate the value of m, we can use the formula below for the slope between two points (x1, y1) and (x2, y2):
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Since x is the number of minutes and C is the cost function, we can use the ordered pairs (x, C). So, using the points (430, 150) and (880, 285), we have:
[tex]m=\frac{285-150}{880-430}=\frac{135}{450}=0.3[/tex]Now, to calculate the value of b, let's use the point (430, 150) in the equation (that is, x = 430 and C = 150):
[tex]\begin{gathered} C=0.3x+b \\ (430,150)\colon \\ 150=0.3\cdot430+b \\ 150=129+b \\ b=150-129 \\ b=21 \end{gathered}[/tex]Therefore the cost function is:
[tex]C=0.3x+21[/tex]B)
Now, to find the cost for 295 minutes, let's use x = 295 and calculate the value of C:
[tex]\begin{gathered} C=0.3\cdot295+21 \\ C=88.5+21 \\ C=109.5 \end{gathered}[/tex]Therefore the cost for 295 minutes is $109.50.