Instructions Unless otherwise stated, show
all work on non graphing problems . Circle all answers. Label and scaleall axes. Each problem, or part, is worth 4 points.
1. A commuter left home, drove toward her
workplace, got some gas, and then continued
driving toward her workplace. Let g
representthe
amount of gas in the gas tank at t
minutes
after the commuter left home. Draw a
qualitative graph of the situation.
Explain any changes in the graph |
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2a, Estimate
y when x =
4.
Since (4, 3) is on the graph, y = 3
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b. Estimat
e x when y
= 2 .
Since (2, 2) is on the graph x = 2 |
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3. Find the slope of the line that passes
through the points (3, -7) and (8, -4). ans. m = 3/5
4. Sketch the graphs of y = - 4
and x =
6.
Label each graph with the equation.
5. Find the x- and y- intercepts of the equation 2x
+ 3y = 12 .
x-intercept: (6, 0)
y-intercept: (0, 4)
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6. Use the graph of the function f to estimate the
fol lowing .
a. Estimate f (- 3) = -2
b. Estimate x
when f (x) = -3 x = -5 |
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7. Let f (x)
= 3x
+ 7 .
a. Find f (3) = 16
b. Find x when f (x) = 2 x = -5/3 |
8. Find the equation of the line passing through the points (-2,
6) and (3, -4).
y = -2x + 2
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9. Some values for a linear equation are given in the
table. Complete the table. There is no work that needs
be shown on this problem.
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10. Consider the model s = 1.70t -112.17 ,
where s
re presents the average salary (in thousands of dollars)
for professors at four-year colleges at t years
since
1900. What is the slope of the model and what does it
mean in this application?
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The salary of 4-year college professors has increased by $1,700 per year.
11. The number of Internet users in the United
States steadily increased over the past
decade. Let n
be the number of Internet
users (in millions) in the United States at t
years since 1995. |
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a. Sketch a scattergram of the data and draw
a “best-fit” line through the data (“eyball”
the line as you did in section 2.1). Label
and scale your axes.
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b. Find the n-intercept
of your linear
model ( simply read it from your graph).
Explain its meaning in this application.
(0, 18.8) – Model predicts
18,800,000 internet users in 1995.
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c. Use your linear model to predict
when all 287 million people in the
United States will be Internet
users (read it from your graph and
mark the point on the graph).
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12. Let
p = f (t
) represent the
percentage of out-of-wedlock
births in the United States for t
years since 1900 (see table).
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a. Find the regression equation for
f (t
) . Write the constants to the
nearest hundredth.
f (t
) =
0.81 t
- 45.86
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b. Find
f (108)
and explain its meaning in this application.
f (108) = 41.62 . In year 2008, the
model predicts 41.6% of births will be out of wedlock.
c. Find the value of t
so that f
(t
) = 43 and explain its meaning in this application. t = 109.7. Model predicts a 43% births will be out of wedlock in
late 2009.
15. Solve by
elimination
16. Solve by any method
dependent system
17. In 2001, the price of a 2001 Cadillac De Ville was $30,055, and the price
for a 2001 Acura Integra was $16,565. The De Ville depreciates by $4391 per
year, and the Integra depreciates by $869 per year. Let
C(t ) and A(t
) represent the values of the Cadillac and Acura, respectively, for
t years since 2001.
a. Write equations for C(t
) and A(t
). C(t
) = 30,055 - 4391t A(t
) = 16,565 - 869t
b. When will the cars have the same value?
What will the value be? t = 3.83 years , the value will be $13,23618. Solve and express the solution in interval notation: 3
- 2(x
- 4) > 4x
+ 1
19. Graph the solution set to the system of inequalities .
