Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
8. Cell Phone Charges One cell phone plan charges a flat monthly rate of
a. Choose letters to represent the variables.
b. Write a formula to express the cell phone charges as a function of the number of text messages (assume that the number is at least
c. Use functional notation to show the cost of the cell phone if you have
d. Write the formula to express the cell phone charges, this assuming that the number of text messages is less than
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Clearance A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down items by 30% each week. This means that each week the cost of an item is 70% of the previous week’s cost. If the original cost of a sofa was $1,000, the cost for the first week would be $1000(0.70) and the cost of the item during the second week would be $1,000(0.70)2. Complete the table shown below. What will be the cost of the sofa during the fifth week? Simplify the expression, to show the cost in dollars.arrow_forwardMortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forwardTax Owed According to the Oklahoma Income Tax Table for 2010, the income tax owed by an Oklahoma resident who is married and filing jointly with a taxable income above 100, 000 is 5070 plus 5.5 of the taxable income over 100, 000. a. Use a formula to express the tax owed as a function of the taxable income, assuming that the taxable income is above 100, 000. Be sure to explain the meaning of the letters you choose and the units. b. What is the tax on a taxable income of 108, 650? Round your answer to the nearest dollar. c. For what taxable income would the tax be 5686?arrow_forward
- Electrical resistance The resistance of a wire varies directly as the length of the wire and inversely as the square of its diameter. A 1000-foot length of wire, 0.05 inch in diameter, has a resistance of 200 ohms. What would be the resistance of a 1500-foot length of wire that is 0.08 inch in diameter.arrow_forwardEarnings Reynalda works as a salesperson in the electronics division of a department store. She earns a base weekly salary plus a commission based on the retail price of the goods she has sold. If she sells x dollars’ worth of goods in a week, her earnings for that week are given by the function E(x)=400+0.03x (a) Find E(2000) and E(15,000) . (b) What do your answers in part (a) represent? (c) Find E(0) . What does this number represent? (d) Find the net change and the average rate of change of her earnings E between x=2000 and x=15,000 . (e) From the formula for E, determine what percentage Reynalda earns on the goods that she sells.arrow_forwardImmigration The following graph shows immigrationin thousand to the United States has varied over the past century. Source: Homeland Security. a. Find the average annual rate of change in immigration for the first half of the century from 1905 to 1955. b. Find the average annual rate of change in immigration for the second half of the century from 1955 to 2005. c. Find the average annual rate of change in immigration for the entire century from 1905 to 2005. d. Average your answers to part a and b, and compare the result with your answer from part c. Will these always be equal for any two time periods? e. If the annual average rate of change for entire century continues, predict the number of immigrants in 2009. Compare answer to the actual number of 1,130,818 immigrants.arrow_forward
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