 Extensions
You are building a hotel on the island and need to plan a sight seeing
tour of the island.
- What
rout will you take around the island to show as many sites as
possible?
- What
sites will you include?
- How
long will the tour take?
- What
is the distance of the tour?
Mathematics
Measurement:
- What
is the perimeter of the island?
- Compare
the highest elevation to the lowest elevation of the island.
- What
is the shortest distance from the lowest elevation to the highest
elevation?
- Where
is the center of the island?
- What
is the farthest distance across the island?
- What
is the shortest distance across the island?
Linear
Functions: The tour bus drives from the hotel to the first
stop on the tour. As the bus drives, the distance from the first
stop depends on the number of minutes the bus has been driving.
When the bus has been driving for 6 minutes, the bus is 17 kilometers
away; when the bus has been driving for 15 minutes, the bus is
11 kilometers away.
Let
y = number of kilometers the bus is from the first stop
Let x = number of minutes the bus has been driving.
Do the following.
- Write
the information about distance and time as two ordered pairs.
- Plot
the two ordered pairs on a Cartesian coordinate system. Remember
which axes are used for dependent and independent variables.
- Assuming
that the distance-time relationship is a linear function, draw
its graph on the Cartesian coordinate system of part b.
- Write
the particular equation of the linear function in part c. Use
the point-slope form.
- Transform
the equation in part d to the slope-intercept form.
- Find
the bus’ distance from the first stop when it has been driving
for 24 minutes by substituting into your equation from part
e.
- Find
the x- and y-intercepts for the function in part
e.
- How
long does it take the bus to get to the first stop. Justify
your answer.
- How
far is the hotel from the first stop? Justify your answer.
Exponential
Functions : Goat problem. When goats were first brought to the
island, hey had no natural enemies so their numbers increased rapidly.
Assume that there were_________ amount of goats in 1865, and that
by 1867 the number had increased to ________. Assume that the number
of goats increases exponentially with the number of years that elapsed
since 1865.
- Write
the particular equation for this function.
- How
many goats would you predict in 1870?
- according
to your model, when was the first pair of goats introduced to
the island?
- Based
on the properties of exponential functions, why is it appropriate
to say that the goats "multiplied"?
- See
The Alien Animals, by George Laycock (Ballantine Books, 1966)
for the eventual outcome of a similar rabbit problem.
Language
Arts
- Keypals
on the Hawaiian Island
- Writing
about a topic
- Hawaiian
language, sayings chants
Social
Studies
Science
- Environmental-
cleaning up solid and chemical waste
- Interrelationship
of plants and animals
- Earth
Sci- erosion control
- Geography
- Food
webs: What animals would you introduce into the food chain to
maintain the a balanced food chain?
Technology
- Research
a topic
- Publish
presentation using presentation software
- Publish
findings on the Internet
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