Eleri Mows Grass In Her Neighborhood. She Charges $ \$35 $ Per Yard. Eleri Offers A Discount To Repeat Customers, Where She Charges $ \$3 $ Less Than The Previous Time To Cut The Grass. Which Explicit Formula Describes How Much She

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Eleri's Lawn Mowing Business: Finding the Explicit Formula for Discounts

Eleri is a diligent lawn mowing professional who offers her services to the residents of her neighborhood. She charges a fixed rate of $35 per yard, but to encourage repeat business, she provides a discount to her loyal customers. The discount is calculated by subtracting $3 from the previous rate each time a customer hires her services. In this article, we will explore the explicit formula that describes how much Eleri charges for lawn mowing services, taking into account the discount she offers to repeat customers.

Let's break down the problem and understand the variables involved. Eleri charges $35 per yard initially. For each subsequent visit, she offers a discount of $3. This means that the cost of lawn mowing services will decrease by $3 each time a customer hires her services. We need to find an explicit formula that describes the cost of lawn mowing services as a function of the number of times Eleri has mowed the lawn.

To develop the explicit formula, we can start by analyzing the pattern of the discounts. The first time Eleri mows the lawn, she charges $35. The second time, she charges $35 - $3 = $32. The third time, she charges $32 - $3 = $29, and so on. We can see that the cost of lawn mowing services decreases by $3 each time.

Let's denote the number of times Eleri has mowed the lawn as n. We can represent the cost of lawn mowing services as a function of n. Since the cost decreases by $3 each time, we can subtract 3 from the initial cost of $35 for each subsequent visit.

The explicit formula can be represented as:

C(n) = 35 - 3(n - 1)

where C(n) is the cost of lawn mowing services for the nth visit.

We can simplify the explicit formula by expanding the expression:

C(n) = 35 - 3n + 3

Combine like terms:

C(n) = 38 - 3n

This is the simplified explicit formula that describes the cost of lawn mowing services as a function of the number of times Eleri has mowed the lawn.

Let's consider some example use cases to illustrate how the explicit formula works.

  • If Eleri has mowed the lawn 1 time, the cost is C(1) = 38 - 3(1) = $35.
  • If Eleri has mowed the lawn 2 times, the cost is C(2) = 38 - 3(2) = $32.
  • If Eleri has mowed the lawn 3 times, the cost is C(3) = 38 - 3(3) = $29.

In this article, we developed an explicit formula that describes the cost of lawn mowing services as a function of the number of times Eleri has mowed the lawn. The formula takes into account the discount she offers to repeat customers, which decreases by $3 each time. We simplified the explicit formula and provided example use cases to illustrate how it works. This formula can be used to calculate the cost of lawn mowing services for any number of visits.

  • None
  • Explore other applications of the explicit formula, such as calculating the total cost of lawn mowing services for a given number of visits.
  • Consider extending the formula to account for other factors, such as the size of the lawn or the frequency of mowing.
    Eleri's Lawn Mowing Business: Q&A

In our previous article, we developed an explicit formula that describes the cost of lawn mowing services as a function of the number of times Eleri has mowed the lawn. The formula takes into account the discount she offers to repeat customers, which decreases by $3 each time. In this article, we will answer some frequently asked questions about Eleri's lawn mowing business and provide additional insights into the explicit formula.

Q: What is the initial cost of lawn mowing services?

A: The initial cost of lawn mowing services is $35 per yard.

Q: How much does the cost decrease each time Eleri mows the lawn?

A: The cost decreases by $3 each time Eleri mows the lawn.

Q: What is the explicit formula that describes the cost of lawn mowing services?

A: The explicit formula is C(n) = 38 - 3n, where C(n) is the cost of lawn mowing services for the nth visit.

Q: How can I use the explicit formula to calculate the cost of lawn mowing services?

A: To calculate the cost of lawn mowing services, simply plug in the number of times Eleri has mowed the lawn (n) into the formula C(n) = 38 - 3n.

Q: What if I want to calculate the total cost of lawn mowing services for a given number of visits?

A: To calculate the total cost, you can multiply the cost of each visit by the number of visits. For example, if Eleri has mowed the lawn 5 times, the total cost would be 5 * C(5) = 5 * (38 - 3(5)) = 5 * 25 = $125.

Q: Can I use the explicit formula to calculate the cost of lawn mowing services for a lawn of a different size?

A: No, the explicit formula is only applicable to lawns of a fixed size (1 yard). If you want to calculate the cost of lawn mowing services for a lawn of a different size, you would need to modify the formula accordingly.

Q: What if Eleri offers a different discount structure?

A: If Eleri offers a different discount structure, you would need to modify the explicit formula to reflect the new discount structure. For example, if Eleri offers a 10% discount each time, the formula would be C(n) = 35 * (1 - 0.1)^n.

In this article, we answered some frequently asked questions about Eleri's lawn mowing business and provided additional insights into the explicit formula. We hope this Q&A article has been helpful in understanding the formula and its applications.

  • None
  • Explore other applications of the explicit formula, such as calculating the total cost of lawn mowing services for a given number of visits.
  • Consider extending the formula to account for other factors, such as the size of the lawn or the frequency of mowing.
  • Develop a more general formula that can be applied to different discount structures and lawn sizes.