t(i, d) dollars is the federal income tax owed by a person who made i dollars and can claim d dependents in a given year. When 2 dependents can be claimed and income is changing, how quickly is the amount of taxes owed changing? (a) Write the mathematical notation for the partial rate-of-change function needed to answer the question posed. ? (b) Write the units of measure for that rate-of-change function. O income dollars O tax dollars per income dollar O income dollars per tax dollar O tax dollars per dependent O income dollars per dependent

EX.1

R² is basically "/" means "divided by" O Variation due to lear function/Total variation O Variation due to linear function/Random variation O Total variation/Variation due to linear function O Random variation/Variation due to linear function

1. A movie theater seats 240 people. For any particular show, the amount of money the theater makes is a function of the number of people, n, in attendance. Analysis of recent price and attendance data suggests that for a weekday matinee showing, if the price of a ticket is set at p dollars, then the number of people in attendance is given by n = 240 – 12p. (a) At what price will no one attend the showing? (b) How many people will attend if prices are set at the regular price of $12? What income will the theater earn at this price? (c) Write an equation that describes the income, I, that the theater will earn in terms of the ticket price, р. (d) At what price should tickets be sold to earn the greatest ticket income from the matinee show? What income will the theater earn at this price?