Project 8.1 Negative Indices
[-4.7, 4.7] by [-3.1, 3.1]
Xscl = 1, Yscl =1
[-4.7, 4.7] by [-3.1, 3.1]
Xscl = 1, Yscl =1
1. To complete the following table proceed as suggested.
a. Press TRACE and use the arrow keys
to complete the second column of the table.
b. Complete column 2 by converting all decimals to fractions.
c. Complete column 3 by rewriting each fraction so that the
denominator is a power of 2.
2. Describe the relationship that exists between the first column
and the last column.
3. State a rule to describe this relationship.
4. What happens to y as x becomes larger?
5. What happens to y as x becomes smaller?
6. When will y approach zero?
Project 8.2 Cooling Down
Pour two cups of water into a kettle and heat it on a stove until the
water begins to boil.
1. Use a thermometer and a stopwatch to complete the following
table:
2. Plot T against t; and draw a line of best fit.
3. Find a rule that relates the temperature, T, to the
time, t.
4. Use the graph to find:
a. the time taken for the water to cool to 70º C
b. the temperature of the water after 22 minutes
c. the temperature of the water after 35 minutes.
5. Verify your answers using your algebraic model.
Your report should include all of your working and diagrams.
Project 8.3 Logarithms
John Napier (1550-1617) of Merchiston, Scotland discovered that indices
make calculations easier and quicker. He defined the logarithm of a
number as an index.
1. Complete the following table:
We can multiply (or divide) numbers using the table of powers of 2.
2. Use the table of powers of 2 to evaluate:
4. Complete the following table:
Compare the computational performance of the different methods.
|
