A landscaping company uses the function c(x)=(600+140 x)/(x) to determine the amount, in dollars

step 1 We need to write an equation for the given scenario that tells us a landscaping company charges

A landscaping company uses the function c(x)=(600+140 x)/(x)...

A landscaping company uses the function $$ c(x)=\frac{600+140 x}{x} $$ to determine the amount, in dollars, it charges per tree to deliver and plant $x$ palm trees. a. Find $c(5)$ and explain what it represents. b. Find $c^{-1}$. c. Use $c^{-1}$ to determine how many palm trees were delivered and planted if the cost per tree was $$\$ 160$$.

A landscaping company uses the function
$$
c(x)=\frac{600+140 x}{x}
$$
to determine the amount, in dollars, it charges per tree to deliver and plant $x$ palm trees.
a. Find $c(5)$ and explain what it represents.
b. Find $c^{-1}$.
c. Use $c^{-1}$ to determine how many palm trees were delivered and planted if the cost per tree was $$\$ 160$$.

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Key Concepts

Application of Inverse Function in Cost Analysis

Using the inverse function in cost analysis helps in determining production or distribution quantities required to meet a specific cost target per unit. This is valuable in decision-making processes where achieving a certain cost efficiency is key, as it translates cost conditions back into quantity decisions.

Inverse Function

An inverse function reverses the relationship between the inputs and outputs of the original function. For a cost function, finding the inverse provides a way to determine the number of items associated with a given cost per item, essentially solving for the input when the output is known.

Cost Function Modeling

A cost function expresses the cost per item as a function of the number of items produced or delivered. It typically includes both fixed costs (that do not depend on the number of items) and variable costs (that do depend on the number produced), allowing for analysis of average cost per unit and optimization decisions.

Function Evaluation

Function evaluation involves substituting a particular input value into the function to obtain the corresponding output value. In the context of cost functions, this means calculating the cost per item when a certain number of items are considered, which helps in understanding pricing and cost distribution.

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