1. The table below shows the cost, C(m), of a taxi ride as a function of the num
ID: 2730646 • Letter: 1
Question
1. The table below shows the cost, C(m), of a taxi ride as a function of the number of miles, m, traveled.
m=
0
1
2
3
4
5
C(m)=
0
7.5
10
12.5
15
17.5
(a) Estimate C(4.50).
C(4.50)= _________
(b) Assume that C is invertible. Estimate C1(13.12).
C1(13.12)= _________
2. Consider the function h(x) given in the following graph
Its domain is _________
Its range is __________
3. New York state income tax is based on taxable income which is part of a person's total income. The tax owed to the state is calculated using taxable income (not total income). In 2005, for a single person with a taxable income between $20,000 and $100,000, the tax owed was $973 plus 6.85% of the taxable income over $20,000. Answer the following questions, and DO NOT include any commas in your final answers.
(a) Compute the tax owed by a person whose taxable income is $49,000.
tax = $______________ (round to nearest dollar)
4. A floor refinishing company charges $1.75 per square foot to strip and refinish a tile floor for up to 1000 square feet. There is an additional charge of $350 for toxic waste disposal for any job which includes more than 150 square feet of tile.
(a) Find an equation for the amount C (in dollars) they will charge to refinish a floor which is x square feet when x150.
C(x)= $________
(b) Find an equation for the amount C (in dollars) they will charge to refinish a floor which is x square feet when x>150.
C(x)= $_________
5. According to the 1993 World Almanac, the number of calories a person walking at 3 mph, bicycling at 10 mph, or swimming at 2 mph burns per minute depends on the person's weight as in the following table.
Calories per minute as a function of weight
Weight (pounds)
100
120
150
170
200
220
Walking (calories)
2.7
3.2
4.0
4.6
5.4
5.9
Bicycling (calories)
5.4
6.5
8.1
9.2
10.8
11.9
Swimming (calories)
5.8
6.9
8.7
9.8
11.6
12.7
(a) Use the table to determine the number of calories that a person weighing 150 pounds uses in an hour of swimming.
6. As dry air moves upward, it expands and in so doing cools at a rate of about 10C for 100m rise, up to about 12 km.
a) If the ground temperature is 250, write a formula for the temperature at height x km.
Answer:
b) What range of temperature can be expected if a plane takes off and reaches a maximum height of 10 km.Write answer in interval notation.
Find the formula for f.
f(x)= ________
8. The obelisk in the movie 2001 has the shape of a rectangular box with lengths x, 4x, and 9x, where x is a parameter.
The volume V of the obelisk is a polynomial expression in x of degree____ and leading coefficient______ .
In fact, V= ______ (enter an expression in x).
Hint: The volume of a brick shaped object equals length times width times height.
m=
0
1
2
3
4
5
C(m)=
0
7.5
10
12.5
15
17.5
Explanation / Answer
1 - a: Equation that best fits the distribution is Y = 2.5X+5 Hence, at 4.5, value of Y = 2.5 *4.5+5 = 16.25 1 - b: Hence, Inverse of that function is (Y-5)/2.5. So value at 13.12 is (13.12-5)/2.5 = 3.248. 2. Domain of given image is , X = [-3,3]. Range is [-2,2]. 3. There is a little ambiguity in the question, which is not made clear. So it is answered considering both assumptions. Taxabale income is 49000. Hence Tax owed is 973+(6.85%*49000) = 4329.5 = 4330. If tax is levied only for amount beyond 20000 only then tax owed = 973+(6.85%(49000-20000)) = 2959.5 = 2960. 4 - a: If x is no. of tiles, then equation is Y = 1.75X, where Y is amount. 4 - b: Equation is Y = 1.75X+350. 5: Calories burnt on swimming per hour, for 150 pound person is 8.7 calories, as per table. 6 - a: If 250 is ground temperature and X is the number of kilometer raise, then best fit equation is Y = 250-100X, where is Y is temperature at X kilometer height. 6 - b: If plane reaches a maximum height of 10 km, replace X in earlier equation at intervals of 1km, 2 km, 3 km etc till 10 KM. 1 (KM) 150 2 50 3 -50 4 -150 5 -250 6 -350 7 -450 8 -550 9 -650 10 -750 7: Here, if intercepts on X-axis and Y-axis are seen, X intercept is -2 and Y intercept is 2. Hence equation is (X/-2) + (Y/2) = 1 means X-Y = -2. 9: Considering the Obelisk with Top side length as x, Bottom side length as 9x and height as 4x. height is derived to be X*(32)^.5 So volume is V = (H/6)*(9X.X+X.9X+2(X.X+9X.9X)) = (91+(2*2^.5))/3 X^2 = 171.39 X^2
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