A utility company charges a base rate for water usage of ...

A utility company charges a base rate for water usage of $\$ 13.50$ per month, plus $\$ 3.58$ for every additional 1000 gal of water used over a 2000 -gal base. a. Write a formula for the monthly charge $C$ for a household that uses $n$ thousand gallons over the 2000-gal base. b. Compute the cost for a family that uses a total of 5000 gal of water for a given month.

A utility company charges a base rate for water usage of $\$ 13.50$ per month, plus $\$ 3.58$ for every additional 1000 gal of water used over a 2000 -gal base.
a. Write a formula for the monthly charge $C$ for a household that uses $n$ thousand gallons over the 2000-gal base.
b. Compute the cost for a family that uses a total of 5000 gal of water for a given month.

Key Concepts

Linear Functions

Linear functions describe relationships in which the change in one variable is directly proportional to the change in another variable, typically represented by a constant rate (slope) and a fixed starting value (y-intercept). They are widely used in modeling real-world situations, such as cost calculations where charges accumulate in proportion to additional usage.

Fixed Cost and Variable Cost

Many practical cost problems are broken down into a fixed cost component, which is constant regardless of usage, and a variable cost component that changes with the level of consumption. This separation helps in formulating cost functions that accurately reflect how initial fees combine with charges based on usage.

Unit Conversion and Interpretation

Accurate problem-solving often depends on correctly interpreting units and ensuring consistency throughout the analysis. When rates are given in specific units (such as per thousand gallons), it is important to convert quantities appropriately so that the defined variables match those units for proper computation.

Cost Function Application

Once the cost function is formulated, it can be used to compute total charges for any given level of usage by substituting the corresponding values into the function. This process involves evaluating the function to combine the fixed and variable costs and arriving at the final cost figure.

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