20. A plumbing company charges $100 for the first hour, $80 for the second hour, and $50 for each additional hour (t ≥ 3). Which equation represents the cost C(t)?
Answer: A
C(t)=180+50(t-2)
The equation representing the cost C(t) for the plumbing company is C(t)=180+50(t-2). This formula accounts for the initial costs for the first two hours and the reduced rate for any additional hours beyond that.
A) C(t)=180+50(t-2)
This option accurately represents the total cost structure. The first hour costs $100, the second hour costs $80, totaling $180 for the first two hours. For each additional hour (t ≥ 3), the cost is $50, which is correctly reflected in this equation.
B) C(t)=100+50(t-2)
This option is incorrect because it only considers the first hour's cost of $100 and applies the additional rate of $50 incorrectly from the second hour onward. It fails to include the correct charge for the second hour, which is $80.
C) C(t)=180+50t
This option is incorrect as it suggests a linear increase in cost without properly accounting for the fixed charges of the first two hours. The equation implies that each hour after the first hour costs $50, which misrepresents the pricing structure.
D) C(t)=100+50t
This equation is also incorrect because it only includes the cost of the first hour as $100 and inaccurately applies the $50 rate to all subsequent hours without recognizing the distinct charge for the second hour.
Conclusion
Option A is the only correct equation as it accurately reflects the tiered pricing model of the plumbing service. The other options miscalculate the costs by either omitting the second hour's charge or applying the additional rate incorrectly. Thus, A is the definitive representation of the cost C(t) based on the provided pricing structure.