8/8/2019 FRQ Problems #1 & #2

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From: Section II, Part A

Time: 30 Minutes2 Questions 

A GRAPHING CALCULATOR IS ALLOWED ON THIS PORTION OF THE EXAM

1.  In a certain count ry, income tax is assessed as f ollows. There is no tax on income up t o $10,000.

Any income over $10,000 is taxed at a rate of 10%, up t o an income of $20,000. Any income

over $20,000 is taxed at 15%.

(a) Write a piecewise f unction f or the tax rate R as a f unction of income I.

(b) Sketch a graph of the tax rate R as a f unction of income I.

(c)  Write a piecewise f unction f or the t otal tax T as a f unction of income I.

(d) Sketch a graph of the t otal tax T as a f unction of income I.

(e) How much tax is assessed on an income of $14,000?

(f)  How much tax is assessed on an income of $26,000?

2.  A small appliance manufact urer finds that it costs $9,000 t o produce 1000 t oasters a week and

$12,000 t o produce 1500 t oasters a week.

(a) Express the cost as a f unction of the number of t oasters produced, assuming that it is

linear. Then sketch the graph.

(b) What is the slope of the graph and what does it represent?

(c)  What is the y-intercept of the graph and what does it represent?

(d) What would the inverse of the f unction in part (a) represent?