Concept explainers
Tax Owed The income tax T owed in a certain state is a function of the taxable income I, both measured in dollars. The formula is
a. Express using functional notation the tax owed on a taxable income of $13, 000, and then calculate that value.
b. If your taxable income increases from
c. If your taxable income increases from
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FUNCTIONS AND CHANGE COMBO
- The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?arrow_forwardA rectangular box is to have a square base and a volume of 30 ft3. The material for the base costs 34¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 25¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box. A rectangular box is shown. The base of the box has length and width each labeled x. The height of the box is labeled y. f(x) =arrow_forwardHourly salary If you earn $225 for 37 1/2 hours of work, how much should you earn for 46 1/2 hours of work at the same rate of pay?arrow_forward
- The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $4000, r = 6.0%, t = 9 months The simple interest owed for the use of the money is $arrow_forwardDifferentiate the function.snip4arrow_forwardThe total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced.The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then…arrow_forward
- The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced.The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then…arrow_forwardThe total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost is $14 per widget (so it costs $14 to produce 1 widget). (a) Use formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.) C = (b) Express using functional notation the total cost there are 225 widgets produced in a month. Calculate the total cost if there are 225 widgets produced…arrow_forwardThe total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative,…arrow_forward
- The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of $7000 per month and that the variable cost is $16 per widget (so it costs $16 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.) C= (b) Express using functional notation the total cost if there are 200 widgets produced in a month. C( |) Calculate the total cost if there are 200…arrow_forwardLondon owes $7, 000 on her credit card. The bank charges an annual interest rate of 16.8%, compounded monthly. If London wants to pay off her credit card using equal monthly payments over the next 18 months, what would the monthly payment be, to the nearest dollar? Pr M 1- (1+r)-" M = the monthly payment P = the amount owed r = the interest rate per month n = the number of paymentsarrow_forwardWrite the surface area as a function of (a) the radius r and (b) the height h.arrow_forward
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