Final answer:
The cost for using 34 HCF of water is $55.81. So, the closest answer is A.
Step-by-step explanation:
To find the cost for using 34 HCF of water, we need to determine the linear function that represents the monthly cost in terms of water used. We can start by finding the slope of the line using the given data points: (17, 37.46) and (55, 100.16). The slope, or the rate of change in cost per unit of water, is calculated as (100.16 - 37.46) / (55 - 17) = 62.7 / 38 = 1.65.
Next, we can use the equation of a linear function, y = mx + b, where y is the cost and x is the water used in HCF, to solve for b, the y-intercept. Plugging in one of the coordinates, 37.46 = 1.65(17) + b, we can solve for b, which is -8.41.
Now that we have the equation of the linear function, y = 1.65x - 8.41, we can plug in 34 for x to find the cost for using 34 HCF of water. Evaluating the equation, we get y = 1.65(34) - 8.41 = 55.81. Therefore, the cost for using 34 HCF of water is $55.81.