Final answer:
To solve for the remaining credit after 76 minutes, we find the rate at which credit decreases using two given data points, establish the linear equation, and substitute 76 for the number of minutes to calculate the remaining credit, which is $17.84.
Step-by-step explanation:
To find the remaining credit after 76 minutes of calls, we first need to establish the rate at which the credit is decreasing based on the two given data points. The remaining credit went from $22.80 after 45 minutes to $19.28 after 67 minutes. This gives us two points: (45, 22.80) and (67, 19.28).
We can calculate the slope of the line (rate of change) using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.
Slope = (19.28 - 22.80) / (67 - 45) = -3.52 / 22 = -$0.16 per minute.
Now, we use point-slope form to find the equation of the line: y - y1 = slope(x - x1). We'll use point (45, 22.80):
y - 22.80 = -0.16(x - 45)
Then, solving for y when x is 76 minutes, we get:
y - 22.80 = -0.16(76 - 45)
y - 22.80 = -0.16(31)
y = 22.80 - 4.96
y = $17.84
Thus, the remaining credit after 76 minutes of calls is $17.84.