Understanding the Sales Functions

Oct 13, 2025 by talynt.org 0 views

Introduction

The table provided shows the sales of plain and Asiago cheese bagels at a bakery for a certain number of hours, denoted as $$h$$. The sales of plain bagels are given by the function $$p(h)$$, while the sales of Asiago cheese bagels are given by the function $$a(h)$$. We are asked to find the difference in sales between Asiago cheese bagels and plain bagels after 6 hours.

Understanding the Sales Functions

To solve this problem, we need to understand the sales functions for plain and Asiago cheese bagels. The sales function for plain bagels is given by $$p(h) = 2h + 5$$, while the sales function for Asiago cheese bagels is given by $$a(h) = 3h + 2$$.

Sales Function for Plain Bagels

The sales function for plain bagels is given by $$p(h) = 2h + 5$$. This function represents the number of plain bagels sold after $$h$$ hours. The coefficient of $$h$$ represents the rate at which plain bagels are sold, while the constant term represents the initial number of plain bagels sold.

Sales Function for Asiago Cheese Bagels

The sales function for Asiago cheese bagels is given by $$a(h) = 3h + 2$$. This function represents the number of Asiago cheese bagels sold after $$h$$ hours. The coefficient of $$h$$ represents the rate at which Asiago cheese bagels are sold, while the constant term represents the initial number of Asiago cheese bagels sold.

Finding the Difference in Sales

To find the difference in sales between Asiago cheese bagels and plain bagels after 6 hours, we need to evaluate the sales functions at $$h = 6$$ and then find the difference between the two values.

Evaluating the Sales Functions at $$h = 6$$

We can evaluate the sales functions at $$h = 6$$ by substituting $$h = 6$$ into the sales functions.

For plain bagels, we have $$p(6) = 2(6) + 5 = 17$$.
For Asiago cheese bagels, we have $$a(6) = 3(6) + 2 = 20$$.

Finding the Difference in Sales

Now that we have evaluated the sales functions at $$h = 6$$, we can find the difference in sales between Asiago cheese bagels and plain bagels.

The difference in sales between Asiago cheese bagels and plain bagels after 6 hours is given by $$a(6) - p(6) = 20 - 17 = 3$$.

Conclusion

In this problem, we were asked to find the difference in sales between Asiago cheese bagels and plain bagels after 6 hours. We used the sales functions for plain and Asiago cheese bagels to evaluate the sales at $$h = 6$$ and then found the difference between the two values. The difference in sales between Asiago cheese bagels and plain bagels after 6 hours is 3.

Discussion

Understanding the Sales Functions

Evaluating the Sales Functions at $$h = 6$$

We can evaluate the sales functions at $$h = 6$$ by substituting $$h = 6$$ into the sales functions.

For plain bagels, we have $$p(6) = 2(6) + 5 = 17$$.
For Asiago cheese bagels, we have $$a(6) = 3(6) + 2 = 20$$.

Finding the Difference in Sales

Now that we have evaluated the sales functions at $$h = 6$$, we can find the difference in sales between Asiago cheese bagels and plain bagels.

The difference in sales between Asiago cheese bagels and plain bagels after 6 hours is given by $$a(6) - p(6) = 20 - 17 = 3$$.

Example Use Case

Suppose the bakery wants to know the difference in sales between Asiago cheese bagels and plain bagels after 8 hours. We can use the sales functions to evaluate the sales at $$h = 8$$ and then find the difference between the two values.

For plain bagels, we have $$p(8) = 2(8) + 5 = 21$$.
For Asiago cheese bagels, we have $$a(8) = 3(8) + 2 = 26$$.

The difference in sales between Asiago cheese bagels and plain bagels after 8 hours is given by $$a(8) - p(8) = 26 - 21 = 5$$.

Conclusion

References

[1] Algebraic Functions. (n.d.). Retrieved from https://www.mathsisfun.com/algebra/functions.html
[2] Sales Functions. (n.d.). Retrieved from https://www.investopedia.com/terms/s/salesfunction.asp

Keywords

Sales functions
Plain bagels
Asiago cheese bagels
Difference in sales
Algebraic functions

Q&A: Understanding the Sales Functions

Q: What is the sales function for plain bagels?

A: The sales function for plain bagels is given by $$p(h) = 2h + 5$$.

Q: What is the sales function for Asiago cheese bagels?

A: The sales function for Asiago cheese bagels is given by $$a(h) = 3h + 2$$.

Q: How do we evaluate the sales functions at a given value of $$h$$?

A: To evaluate the sales functions at a given value of $$h$$, we substitute the value of $$h$$ into the sales functions. For example, to evaluate the sales functions at $$h = 6$$, we substitute $$h = 6$$ into the sales functions.

Q: How do we find the difference in sales between Asiago cheese bagels and plain bagels?

A: To find the difference in sales between Asiago cheese bagels and plain bagels, we evaluate the sales functions at the given value of $$h$$ and then find the difference between the two values. For example, to find the difference in sales between Asiago cheese bagels and plain bagels after 6 hours, we evaluate the sales functions at $$h = 6$$ and then find the difference between the two values.

Q&A: Evaluating the Sales Functions at $$h = 6$$

Q: What is the value of $$p(6)$$?

A: The value of $$p(6)$$ is given by $$p(6) = 2(6) + 5 = 17$$.

Q: What is the value of $$a(6)$$?

A: The value of $$a(6)$$ is given by $$a(6) = 3(6) + 2 = 20$$.

Q: What is the difference in sales between Asiago cheese bagels and plain bagels after 6 hours?

A: The difference in sales between Asiago cheese bagels and plain bagels after 6 hours is given by $$a(6) - p(6) = 20 - 17 = 3$$.

Q&A: Finding the Difference in Sales

Q: How do we find the difference in sales between Asiago cheese bagels and plain bagels after 8 hours?

A: To find the difference in sales between Asiago cheese bagels and plain bagels after 8 hours, we evaluate the sales functions at $$h = 8$$ and then find the difference between the two values.

Q: What is the value of $$p(8)$$?

A: The value of $$p(8)$$ is given by $$p(8) = 2(8) + 5 = 21$$.

Q: What is the value of $$a(8)$$?

A: The value of $$a(8)$$ is given by $$a(8) = 3(8) + 2 = 26$$.

Q: What is the difference in sales between Asiago cheese bagels and plain bagels after 8 hours?

A: The difference in sales between Asiago cheese bagels and plain bagels after 8 hours is given by $$a(8) - p(8) = 26 - 21 = 5$$.

Conclusion

In this Q&A article, we have discussed the sales functions for plain and Asiago cheese bagels, evaluated the sales functions at $$h = 6$$ and $$h = 8$$, and found the difference in sales between Asiago cheese bagels and plain bagels after 6 hours and 8 hours.

References

[1] Algebraic Functions. (n.d.). Retrieved from https://www.mathsisfun.com/algebra/functions.html
[2] Sales Functions. (n.d.). Retrieved from https://www.investopedia.com/terms/s/salesfunction.asp

Keywords

Sales functions
Plain bagels
Asiago cheese bagels
Difference in sales
Algebraic functions