Enviro-Safe Pest Management charges new clients 150 for an...

Enviro-Safe Pest Management charges new clients $\$ 150$ for an in-home inspection and initial treatment for ants. Monthly preplanned treatments cost $\$ 38$. a. Write an equation for the total cost for pest management from Enviro-Safe Pest Management depending on the number of months a house is treated. b. If the house has an initial treatment and then is treated monthly for 1.5 more years, how much will Enviro-Safe charge?

Enviro-Safe Pest Management charges new clients $\$ 150$ for an in-home inspection and initial treatment for ants. Monthly preplanned treatments cost $\$ 38$.
a. Write an equation for the total cost for pest management from Enviro-Safe Pest Management depending on the number of months a house is treated.
b. If the house has an initial treatment and then is treated monthly for 1.5 more years, how much will Enviro-Safe charge?

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Key Concepts

Cost Function

A cost function is an expression that calculates the total cost based on certain input variables, such as time or quantity. It typically accounts for both fixed and variable costs. This concept is crucial for determining how overall expenses are built up from an upfront fee combined with ongoing charges.

Fixed and Variable Costs

Fixed costs are constant and do not change with the level of activity, such as an initial service fee, while variable costs change proportionally with the number of periods or units, like monthly fees. Understanding this distinction is essential for correctly formulating equations that explain total cost accumulation over time.

Linear Equation

A linear equation represents a straight-line relationship between two variables, typically expressed in the form y = mx + b. In this context, it models the total cost as a function of time, where the slope (m) represents the recurring cost per month and the intercept (b) represents the initial fixed cost.

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