T fu ar S r 1 2. A man has an annual (salary) income of $60,437 from his job. His daughter is 2 years old when he sets up a college fund for her with his credit union. His initial deposit is $2000 (in honor of her 2nd birthday). He expects her to go to college when she turns 18, and hopes that this scheme will generate sufficient funds. (a) He decides to put 8.0% of his weekly salary into this fund every week from her 2nd birthday until she turns 18 years old. (Assume he never gets a raise during this period of time, so his deposits remain constant.) Let w = the number of weeks since his daughter's 2nd birthday, and let B = the balance of her college fund (excluding any interest it might earn over this time period). Find a linear equation that mathematically finds the relationship between these two variables. (Use 1 year = 52 weeks.) EQUATION: (b) Interpret the values of the slope and the vertical intercept of your equation (with dimensional units) in the context of this problem. (c) Use the equation to determine the balance of the daughter's college fund on her 12th birthday and on her 18th birthday (excluding interest earned). (Assume 1 year = 52 weeks.) Round (if needed) to the nearest $0.01 and include dimensional units with your final answers. OD 11 Balance on 12th birthday = Balance on 18th birthday 3. Suppose a manufacturer makes and sells a product that costs $8.75 per item. The fixed costs (that do not depend on the number of items made) are $12,535. Each item sells for $14.50. Determine how many items must be made and sold in order to "break even" - meaning the total costs of manufacturing equals the total revenue from sales. Show your supporting work, including how you defined your variable(s) / function(s).
T fu ar S r 1 2. A man has an annual (salary) income of $60,437 from his job. His daughter is 2 years old when he sets up a college fund for her with his credit union. His initial deposit is $2000 (in honor of her 2nd birthday). He expects her to go to college when she turns 18, and hopes that this scheme will generate sufficient funds. (a) He decides to put 8.0% of his weekly salary into this fund every week from her 2nd birthday until she turns 18 years old. (Assume he never gets a raise during this period of time, so his deposits remain constant.) Let w = the number of weeks since his daughter's 2nd birthday, and let B = the balance of her college fund (excluding any interest it might earn over this time period). Find a linear equation that mathematically finds the relationship between these two variables. (Use 1 year = 52 weeks.) EQUATION: (b) Interpret the values of the slope and the vertical intercept of your equation (with dimensional units) in the context of this problem. (c) Use the equation to determine the balance of the daughter's college fund on her 12th birthday and on her 18th birthday (excluding interest earned). (Assume 1 year = 52 weeks.) Round (if needed) to the nearest $0.01 and include dimensional units with your final answers. OD 11 Balance on 12th birthday = Balance on 18th birthday 3. Suppose a manufacturer makes and sells a product that costs $8.75 per item. The fixed costs (that do not depend on the number of items made) are $12,535. Each item sells for $14.50. Determine how many items must be made and sold in order to "break even" - meaning the total costs of manufacturing equals the total revenue from sales. Show your supporting work, including how you defined your variable(s) / function(s).
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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2. A man has an annual (salary) income of $60,437 from his job. His daughter is 2 years old when he sets up a
college fund for her with his credit union. His initial deposit is $2000 (in honor of her 2nd birthday). He
expects her to go to college when she turns 18, and hopes that this scheme will generate sufficient funds.
(a) He decides to put 8.0% of his weekly salary into this fund every week from her 2nd birthday until she turns
18 years old. (Assume he never gets a raise during this period of time, so his deposits remain constant.)
Let w = the number of weeks since his daughter's 2nd birthday, and
let B = the balance of her college fund (excluding any interest it might earn over this time period).
Find a linear equation that mathematically finds the relationship between these two variables.
(Use 1 year = 52 weeks.)
EQUATION:
(b) Interpret the values of the slope and the vertical intercept of your equation (with dimensional units) in the
context of this problem.
(c) Use the equation to determine the balance of the daughter's college fund on her 12th birthday and on her 18th
birthday (excluding interest earned). (Assume 1 year = 52 weeks.) Round (if needed) to the nearest $0.01
and include dimensional units with your final answers.
Balance on 12th birthday =
Balance on 18th birthday =
3. Suppose a manufacturer makes and sells a product that costs $8.75 per item. The fixed costs (that do not
depend on the number of items made) are $12,535. Each item sells for $14.50. Determine how many items
must be made and sold in order to "break even" - meaning the total costs of manufacturing equals the total
revenue from sales. Show your supporting work, including how you defined your variable(s) / function(s).
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