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3) Let A(T) be the function that gives the pounds of food ordered when the total is $T. a. Find a function equation for A(T). b. Show that the function A(T) is the inverse of the function H (P). C. Use A(T) to find the most food Sully can get when spending $300 or less.

3) Let A(T) be the function that gives the pounds of food ordered when the total is $T. a. Find a function equation for A(T). b. Show that the function A(T) is the inverse of the function H (P). C. Use A(T) to find the most food Sully can get when spending $300 or less.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you show the work and explain your reasoning for the 3rd question. 

Cheddar's favorite online dogfood retailor charges $8 per pound of food, $12 for flat rate shipping (on any size order), and there is a 9% tax that applies to both the price of food and the shipping price. Orders can be placed as few as 10 pounds, as much as 100 pounds, or any multiple of 5 pounds in between 10 and 100. 1) Let F(P) be the subtotal, in dollars, when P pounds of food are ordered. The subtotal F(P) does not include the cost of shipping or tax. a. Give a function equation for F(P). b. Give the domain and range of F(P) (include correct units). c. Find and interpret F(45). 2) Let T be the order total in dollars. The total T does include the cost of shipping and tax. a. Give the total, G (S), as a function of the subtotal, S, by writing a function equation for T = G(S). b. Give the total T, as a function of the pounds of food ordered, P, by writing a function equation for the composition H(P) = G(F(P)). c. Find and interpret G(45). d. Find the cheapest total possible. e. Find the most expensive total possible. %3! 3) Let A(T) be the function that gives the pounds of food ordered when the total is $T. a. Find a function equation for A(T). b. Show that the function A(T) is the inverse of the function H(P). Use A(T) to find the most food Sully can get when spending $300 or less. C.
Transcribed Image Text:Cheddar's favorite online dogfood retailor charges $8 per pound of food, $12 for flat rate shipping (on any size order), and there is a 9% tax that applies to both the price of food and the shipping price. Orders can be placed as few as 10 pounds, as much as 100 pounds, or any multiple of 5 pounds in between 10 and 100. 1) Let F(P) be the subtotal, in dollars, when P pounds of food are ordered. The subtotal F(P) does not include the cost of shipping or tax. a. Give a function equation for F(P). b. Give the domain and range of F(P) (include correct units). c. Find and interpret F(45). 2) Let T be the order total in dollars. The total T does include the cost of shipping and tax. a. Give the total, G (S), as a function of the subtotal, S, by writing a function equation for T = G(S). b. Give the total T, as a function of the pounds of food ordered, P, by writing a function equation for the composition H(P) = G(F(P)). c. Find and interpret G(45). d. Find the cheapest total possible. e. Find the most expensive total possible. %3! 3) Let A(T) be the function that gives the pounds of food ordered when the total is $T. a. Find a function equation for A(T). b. Show that the function A(T) is the inverse of the function H(P). Use A(T) to find the most food Sully can get when spending $300 or less. C.
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