Let's transcribe and solve the problem step by step. --- ## Problem Transcription "The primary cost (in dollars) of water use is the tower blowdown (the removal of water needed to prevent scale formation and corrosion of boiler tubes, HCT). The cost for using 2 HCT of water is $17.41 and the cost for using 3 HCT is $18.97. **(a) What is the cost after using 2.50 HCT of water?**" --- ## Step-by-Step Solution We are told the cost for: - 2 HCT = $17.41 - 3 HCT = $18.97 We are to find the cost for 2.50 HCT. ### Step 1: Recognize the Relationship Assume the cost varies linearly between the two points (since no other information is given). ### Step 2: Find the Slope (Cost per HCT) \[ \text{Slope} = \frac{\text{Change in Cost}}{\text{Change in HCT}} = \frac{18.97 - 17.41}{3 - 2} = \frac{1.56}{1} = 1.56 \text{ dollars per HCT} \] ### Step 3: Find the Cost at 2.50 HCT From 2 HCT to 2.50 HCT is an increase of 0.5 HCT. \[ \text{Additional Cost} = 0.5 \times 1.56 = 0.78 \] \[ \text{Total Cost at 2.50 HCT} = \text{Cost at 2 HCT} + \text{Additional Cost} \] \[ = 17.41 + 0.78 = 18.19 \] --- ## **Final Answer** **The cost after using 2.50 HCT of water is $\boxed{18.19}$ dollars.**