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CHAPTER 5
Preparing for Assessment
Performance Task
Provide a clear solution to each part of the task. Be sure to show all of your work, include all
relevant drawings, and justify your answers.
Part A
After studying production of two different varieties of tomatoes grown in two identical
gardens, Ravi comes up with the following equations to represent the tomatoes’ production rates:
Variety A:
t
=
2
d
2
+
4
d
-
2 Variety B:
t
=
d
2
+
d
+
1
In Ravi’s models,
t
represents the total number of tomatoes produced in each garden and
d
represents the number of whole days since the plants first started producing tomatoes.
• Write an expression that models the total production rates of both varieties.
• Determine which variety is more productive. Explain your reasoning.
• Write an expression that models how much more productive
one variety is than the other.
Part B
While studying the decline of a certain kind of cell in children with certain illnesses,
Ravi calculates the following functions to represent how the decrease in the numbers of cells
c
as a function of the number of days
d
the child has the illness:
Illness A:
c
1
(
d
)
=
1218
e
-
0.05
d
Illness B:
c
2
(
d
)
=
420
e
-
0.125
d
Ravi also finds that if a child has
both
illnesses, because of the increased trauma to the immune
system, the total decrease in cells is the product of the two functions, rather than the sum.
• Write a function that models the decrease in the number of cells if a child
had
both
illnesses.
Part C
Ravi is working with data collected by researchers all over the world concerning
bacteria growth in different bodies of water with different temperatures. The data collected is
in Kelvin, Celsius, and Fahrenheit. The formula to convert Kelvin to Celsius is
T
(
C
)
=
T
(
K
)
-
273.15,
and the formula to convert Celsius to Fahrenheit is
T
(
F
)
=
9
_
5
T
(
C
)
+
32.
• Write a composition function that can be used to directly convert Kelvin to Fahrenheit.
Part D
Johanna is working on a project involving asteroids stuck in the orbit of a planet.
The formula for escape velocity is
v
≥
√
2
GM
_
r
, where
v
is the necessary velocity needed to
escape orbit,
G
is the gravitational constant,
M
is the mass of the planet, and
r
is the radius
of the planet. The gravitational constant is 6.673
×
10
-
11
.
• If the mass of the Earth is 5.98
×
10
24
, in kilograms, and the escape velocity needed for
an asteroid to leave Earth’s orbit is 11,184 meters per second, determine the radius of
the Earth. (Note: do not worry about units.)
Part E
Johanna next turns her focus to a project involving springs. The period of oscillation of a
spring can be found using the formula
T
=
2
π
√
m
_
k
, where
T
is the period,
m
is the mass of
the oscillating body, and
k
is a constant.
• Write an equation for the mass of the oscillating body, in terms of the period.
APPLY MATH
Two students at a university are each research assistants. Johanna is a physics research assistant and
Ravi is a biology research assistant. They are both performing various calculations on data collected in their labs.
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Chapter 5
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Performance Task