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At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f(n) represents the total cost of shoe rental and n games, what is the recursive equation for f(n)? Of(n) = 2.75 +4.75 + f(n − 1), f(0) = 2.75 Of(n) = 4.75 + f(n-1), f(0) = 2.75 Of(n)=2.75 +4.75n, n > 0 Of(n) = (2.75 +4.75)n, n > 0

At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f(n) represents the total cost of shoe rental and n games, what is the recursive equation for f(n)? Of(n) = 2.75 +4.75 + f(n − 1), f(0) = 2.75 Of(n) = 4.75 + f(n-1), f(0) = 2.75 Of(n)=2.75 +4.75n, n > 0 Of(n) = (2.75 +4.75)n, n > 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem Statement At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If \( f(n) \) represents the total cost of shoe rental and \( n \) games, what is the recursive equation for \( f(n) \)? ### Options 1. \( f(n) = 2.75 + 4.75 + f(n - 1), f(0) = 2.75 \) 2. \( f(n) = 4.75 + f(n - 1), f(0) = 2.75 \) 3. \( f(n) = 2.75 + 4.75n, n > 0 \) 4. \( f(n) = (2.75 + 4.75)n, n > 0 \) ### Explanation This problem involves calculating the total cost of bowling, including a constant shoe rental fee and a variable cost per game. The recursive equation must account for the initial shoe rental fee at \( n = 0 \) and the cost per game for each subsequent game. **1. Option 1:** - This equation incorrectly adds the shoe rental and the first game cost for each recursive call. - \( f(n) = 2.75 + 4.75 + f(n - 1), f(0) = 2.75 \) **2. Option 2:** - This option correctly represents the total cost with the base case \( f(0) \) incorporating the shoe rental cost, and each recursive step adding the cost per game. - \( f(n) = 4.75 + f(n - 1), f(0) = 2.75 \) **3. Option 3:** - This option is a direct equation but not a recursive one. It correctly adds the shoe rental and total game costs for \( n > 0 \). - \( f(n) = 2.75 + 4.75n, n > 0 \) **4. Option 4:** - This option incorrectly multiplies the sum of shoe rental and cost per game by \( n \). - \( f(n) = (2.75 + 4.75)n, n > 0 \) The correct recursive equation is **Option 2**: \[ f(n) =
Transcribed Image Text:### Problem Statement At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If \( f(n) \) represents the total cost of shoe rental and \( n \) games, what is the recursive equation for \( f(n) \)? ### Options 1. \( f(n) = 2.75 + 4.75 + f(n - 1), f(0) = 2.75 \) 2. \( f(n) = 4.75 + f(n - 1), f(0) = 2.75 \) 3. \( f(n) = 2.75 + 4.75n, n > 0 \) 4. \( f(n) = (2.75 + 4.75)n, n > 0 \) ### Explanation This problem involves calculating the total cost of bowling, including a constant shoe rental fee and a variable cost per game. The recursive equation must account for the initial shoe rental fee at \( n = 0 \) and the cost per game for each subsequent game. **1. Option 1:** - This equation incorrectly adds the shoe rental and the first game cost for each recursive call. - \( f(n) = 2.75 + 4.75 + f(n - 1), f(0) = 2.75 \) **2. Option 2:** - This option correctly represents the total cost with the base case \( f(0) \) incorporating the shoe rental cost, and each recursive step adding the cost per game. - \( f(n) = 4.75 + f(n - 1), f(0) = 2.75 \) **3. Option 3:** - This option is a direct equation but not a recursive one. It correctly adds the shoe rental and total game costs for \( n > 0 \). - \( f(n) = 2.75 + 4.75n, n > 0 \) **4. Option 4:** - This option incorrectly multiplies the sum of shoe rental and cost per game by \( n \). - \( f(n) = (2.75 + 4.75)n, n > 0 \) The correct recursive equation is **Option 2**: \[ f(n) =
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