Transcript MATH 109 Test 3 Review

MATH 109 Test 3 Review
Jeopardy
Potent
Potables
Quad Apps
Quads
Potpourri
100
100
100
100
200
200
200
200
300
300
300
300
400
400
400
400
500
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500
Potpourri 100
• Suppose that a quadratic function has a
maximum at its vertex at the point (-5, 22).
How many zeros does the quadratic
function have?
• Answer: 2
Potpourri 200
• Find an equation for a quadratic function
that does not cross the x-axis and has a
negative vertical intercept
• Answers will vary
Potpourri 300
• When rabbits were first brought to
Australia, they multiplied very rapidly
because there were no predators. In
1865, there were 60,000 rabbits. By 1867,
there 2,400,000 rabbits. Assuming
exponential growth, when was the first pair
of rabbits introduced into the country?
• Answer: Around 1859
Potpourri 400
• The consumer price index compares the cost of
goods and services over various years. The
base year for comparison is 1967. The same
goods and services that cost $100 in 1967 cost
$184.50 in 1977. Assuming that costs increase
exponentially, when did the same goods and
services cost double that of 1967?
• Answer: 1978
Potpourri 500
• When a murder is committed, the temperature of the body cools
according to the equation:
H  22  15e
rt
• Suppose after two hours, the body cools to 35 degrees C. Find r .
• r = -0.7155
• Suppose the police find a dead body with a temperature of 30
degrees C at 4 pm. Use this information to determine when the
murder was committed?
• Answer: 7:13am
Potent Potables 100
• Plutonium, the fuel for atomic weapons, has a
half-life of 24,400 years. Most atomic weapons
are designed with a 1% mass margin. This
means the weapon will remain functional until
the original fuel has decayed more than 1%
(leaving 99% of the original amount). Estimate
how many years a plutonium bomb would
remain functional.
• About 354 years
Potent Potables 200
• The proportion of carbon-14, an isotope of
carbon, in living plant matter is constant. Once a
plant dies, the carbon-14 in it begins to decay
with a half-life of 5570 years. An archaeologist
measures the remains of carbon-14 in a
prehistoric hut and finds it to be one-tenth the
amount of carbon-14 in the living wood. How
old is the hut?
• Answer: 18,503 years old
Potent Potables 300
• Solve for x: log 2 3  x   log 2  x   2
• Answer: x = -1
Potent Potables 400
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During a hot summer day, the air conditioning
unit in your apartment goes out. The time, t, in
hours after your AC went out is given by the
equation:
 105  H 
t  5.944  ln 

 35 
where H is the temperature (in degrees
Fahrenheit) of your apartment at that time.
What is the temperature of your apartment
when your AC goes out?
About 70 degrees F
Potent Potables 500
• The population of a town was initially
10,000 and grew to 15,000 in 5 years.
Assuming exponential growth complete
the table given below:
y  C a 
y  Ce
x
rx
y  10000 1.084 
x
y  10000 e
0.0811x
y  C 2
x
d
y  10000 2
x
8.55
Quads 100
• Find an equation for a quadratic function
with vertex (h,k) where h < 0 and k > 0 and
has a positive y-intercept.
• Answers will vary
Quads 200
• Find the equation of a quadratic function
with zeros at 2 and -4 and passing through
the point (0,4).
1
y   x  2x  4
2
Quads 300
• For the quadratic function graphed below,
find (i) an equation (ii) the vertex (iii) focal
point
y
5
x  2x  6
12
20 

Vertex :   2, 
3

91 

Focus :   2, 
15 

Quads 400
• Rewrite the following quadratic in vertex
form: y  3x 2  18 x  9
• Find the zeros of this quadratic function.
y  3x  3  18
• Vertex:
• Zeros: 0.551 and 5.450
2
Quads 500
• A quadratic function f(x) has vertex at (2,k)
where k is a real number, and passes
through the point (-1,3). Explain under
what conditions this function would have
no x-intercepts. Determine the values of k
so that f(x) has no x-intercepts
• 0<k<3
Quad Applications 100
• A horticulturist has determined that the
number of inches a young redwood tree
grows in one year is a function of the
annual rainfall, r (in inches), given by:
g r   0.02r  r  1
2
• What is the maximum number of inches a
young redwood can grow in a year?
• 13.5 inches
Quad Applications 200
• A stone thrown downward with an initial velocity
of 49 m/s will travel a distance of s meters
according to the function
st   4.9t 2  49t
• Where t is measure in seconds.
• If a stone is thrown downward with an initial
velocity of 49 m/s from a height of 274.4 meters,
how long until the stone hits the ground?
• 4 seconds
Quad Applications 300
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A slim line fluorescent bulb with ½ inch diameter needs 1 inch clearance top
and bottom in a parabolic reflecting shade.
What are the coordinates of the focus?
(0, -1.25)
What is the equation for this reflector?
1
y   x2
5
• What is the diameter of the opening of the shade?
• 7.07 ft
Quad Applications 400
• A bakery sells specialty pies during a six month
period. In order to make the most money, the
bakery changes the price of the pies to see how
sales are affected. Month Number Sold Price
1
2
3
4
5
6
300
350
400
450
500
550
13
12
11
10
9
8
• How many pies should they sell and at what
price to make the most money?
• 475 pies at $9.50 per pie
Quad Applications 500
• A diary farmer has 1500 feet of fencing. He
wants to use all 1500 feet to construct a
rectangle and two interior separators that
together make three rectangular pens.
• Determine the dimensions of the larger
rectangle that gives the maximum area.
• L = 375 ft W = 187.5 ft