Year 12 AAHL1 Polynomials Performance Task PDF
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Summary
This document is a mathematics past paper for year 12 students, focusing on polynomials and their applications in business contexts. Students are required to analyze revenue, cost, and profit functions, and evaluate the feasibility of launching a new product. The paper delves into concepts like intercepts, local extrema, and asymptotes to provide a complete mathematical model for business decisions.
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YEAR 12 AAHL1 - POLYNOMIALS PERFORMANCE TASK: Polynomials For this assignment you and a partner will take on the roles of CFO (Chief Financial Officers) of your company. The staffs in the accounting and production departments have sent you their models regarding the launch of a new exciting product...
YEAR 12 AAHL1 - POLYNOMIALS PERFORMANCE TASK: Polynomials For this assignment you and a partner will take on the roles of CFO (Chief Financial Officers) of your company. The staffs in the accounting and production departments have sent you their models regarding the launch of a new exciting product. Your job as CFO is to write a report discussing the merits of launching this new product. MAIN TASK: The accounting team has sent you a Revenue Function R(t) which models the amount of money (in US dollars) collected by the sales of the new product over the time (in days) following its launch: The production team has also sent you a Cost Function C(t) which models the amount of money (in US dollars) required to cover the cost of production of the product over the time (in days) following its launch: 1. Graph and label the revenue and cost functions on two separate sets of axes using technology. 2. Find and discuss the significance of the intercept(s), local maxima, and local minima in the context of the business for both models. Be sure to label these significant points on your graph. 3. Find, graph, and label the profit function on a separate set of axes using technology. The Profit Function P(t): 4. Find and discuss the significance of the intercept(s), local maxima, and local minima of the profit function in the context of the business. Be sure to label these significant points on your graph. 5. Does the end behavior of the functions R(t), C(t), and P(t) make sense? How would you modify these models in order to improve them contextually? 6. Using the information in Part 1, is this product worth launching? Why or why not? EXTENSION TASK: The production team has also sent you a numbers function which models the number of units of the product that the factory will produce over the time (in days) following its launch. 1. Graph and label the numbers function N(t) on a separate set of axes using technology. 2. Find and discuss the significance of the intercept(s), local maxima, and local minima of the numbers function in the context of the business. Be sure to label these significant points on your graph. 3. Find, graph, and label the average profit function, on a separate set of axes using technology. 4. Find and discuss the significance of the intercept(s), local maxima, local minima, and asymptotes of the average profit function in the context of the business. Be sure to label these significant points and asymptotes on your graph. 5. Does the end behavior of the functions N(t) and A(t) make sense? How would you modify these models in order to improve them contextually? Using the information in this part to decide if it is worth launching this product in your report?
