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: A Modeling Approach to College Algebra (MindTap Course List)
- Juice Sales The number J, in thousands, of cans of frozen orange juice sold weekly is a function of the price P, in dollars, of a can. In a certain grocery store, the formula is J=11-2.5P. a. Express using functional notation the number of cans sold weekly if the price of a can is 1.40, and then calculate that value. b. At what price will there be 7.25 thousand cans sold weekly? c. Solve for P in the formula above to obtain a formula expressing P as a fuction of J. d. At what price will there be 7.75 thousand cans sold weekly?arrow_forwardm Miles per Gallon The cost of operating a car depends on the gas mileage in that your car gets, the cost x per gallon of gasoline, and the distance d that you drive. a. How much does it cost to drive 100 miles if your car gets 25 miles per gallon and gasoline costs 349 cents per gallon? b. Find a formula that gives the cost C as a function of m, g, and d be sure to state the units of each variable. c. Use functional notation to show the cost of driving a car that gets 28 miles per gallon a distance of 138 miles if gasoline costs 3.69 per gallon Use the formula from part b to calculate the cost.arrow_forwardFalling with a parachute If an average-sized man jumps from an airplane with an open parachute, his downward velocity t seconds into the fall is v(t)=20(10.2t) Feet per second. a. Use functional notation to express the velocity 2 seconds into the fall, and then calculate it. b. Explain how the velocity increases with time. Include in your explanation the average rate of change from the beginning of the fall to the end of the first second and the average rate of change from the fifth second to the sixth second of the fall. c. Find the terminal velocity. d. Compare the time it takes to reach 99 of terminal velocity here with the time it took to reach 99 of terminal velocity in Example 2.1. On the basis of the information we have, which would you expect to reach 99 of terminal velocity first, a feather or a cannonball?arrow_forward
- Gross Profit Margin The gross profit margin is a measurement of a companys manufacturing and distribution efficiency during the production process. If G is the gross profit and T is the total revenue, both in dollars, then the gross profit margin M=M(G,T) is given by the formula M=GT a. Use functional notation to express the gross profit margin for a company that has a gross profit of 335, 000 and a total revenue of 540, 000. b. Calculate the gross profit margin in part a. The gross profit margin is often expressed as a percent. Give your answer as both a decimal and a percent. c. If the gross profit stays the same but total revenue increases, would the gross profit margin increase or decrease?arrow_forwardRunning Ants A scientist observed that the speed S at which certain ants ran was a function of T, the ambient temperature. He discovered the formula S=0.2T-2.7, Where S is measured in centimetres per second and T is in degrees Celsius. a. Using functional notation, express the speed of the ants when the ambient temperature is 30 degrees Celsius, and calculate that speed using the formula above. b. Solve for T in the formula above to obtain a formula expressing the ambient temperature T as a function of the speed S at which the ants run. c. If the ants are running at a speed of 3 centimeters per second, what is the ambient temperature?arrow_forwardMilk Production Milk production M (in billions of pounds) in the United States from 2000 through 2014 can be modeled by M=3.00t+163.3,0t14 where t represents the year, with t = 0 corresponding to 2000. (a) According to the model, when was the annual milk production greater than 180 billion pounds, but no more than 190 billion pounds? (b) Use the model to predict when milk production will exceed 230 billion pounds.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning