Final answer:
To find the remaining credit after 36 minutes of calls, we set up a system of equations using the given data. Solving the system, we find the equation of the linear function and calculate the remaining credit. The correct answer is $14.95.
Step-by-step explanation:
To find the remaining credit after 36 minutes of calls, we need to determine the equation of the linear function that represents the relationship between the remaining credit and the total calling time.
Let's use the given information to set up a system of equations. We know that after 21 minutes of calls, the remaining credit is $17.27 and after 34 minutes of calls, the remaining credit is $15.58.
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1)
where (x1, y1) = (21, 17.27) and (x, y) represents any point on the line.
Substituting the known values, we have:
y - 17.27 = m(x - 21)
Similarly, for the point (34, 15.58), we have:
y - 15.58 = m(x - 34)
Solving the system of equations, we find that m = -0.37 and the equation of the linear function is y = -0.37x + 24.17.
Finally, substituting x = 36 into the equation, we can calculate the remaining credit after 36 minutes of calls:
y = -0.37(36) + 24.17 = $14.95
Therefore, the remaining credit after 36 minutes of calls is $14.95. So the correct answer is option b) $14.95.