Question

Quiz 1 Name: 1. The income tax Towed in a certain state is a function of the taxable income I, both measured in dollars. The formula is 1 0.101 - 700 a. Express using function notation the tax owed on a taxable income of $15,000 and then calculate that value. b. If your taxable income increases from $15,000 to $20,000, how much does your tax increase by? 2. The following table shows the US gross domestic product (GDP) G, in trillions of dollars, as a function of the year y. y-Year 2004 2010 2014 G GDP in trillions 11.8714.66 17.42 of dollars) a. Explain what G(2004) means b. Use function notation to express the GDP in 2007 and then estimate its value. 3. Describe the following graph. Be sure to specifically mention its concavity and whether it is increasing or decreasing. Then, evaluate it (give the output) at x -2.

Answer 1

1(a).The functional notation is given by -

T=0.10(I)-700 And its value if taxable income is $ 15000

T= 0.10(15000)-700=$800

1(b) if taxable income increase to $ 20000, the value is

T=0.10(20000)-700=$ 1300

the increase in the T( Income Tax ) is $500

2(a) G(2004) means country domestic product in trillions of dollars in the year 2004

2(b) growth rate =% change in GDP that is

Growth rate = GDP in 2010- GDP in 2004

GDP IN 2010

= 14.66-11.87/11.87*100

= 23.50%

AVERAGE RATE OF INCREASE FOR THE PERIOD 2004 TO 2010 IS 3.91%

CUMULATIVE GROWTH RATE DURING THE PERIOD 2004 TO 2007 11.73%

THE FUNCTIONAL NOTATION TO EXPRESS GDP IN 2007

X REPRESENT GDP 2004

Y(2007)=X+.1173(X)

=11.87+.1173(11.87)

= 13.26

4. THE FUNCTION NOTATION TO REPRESENT THE TOTAL COST TO PRODUCE DIAMOND

y= x+4(z)

y Represent the total cost

x Represent  raw material cos

z Represent cost per hour of diamond cutter

Y= $100+4($32)= $228