The Bouncing Ball

A good resource for learning your way around the calculator or
to review what we've learned in class ...
Working with Sequences on the TI-83+ or 84+
http://www.mathbits.com/MathBits/TISection/PreCalculus/sequences.htm

Geometic Sequence:
(i) Recursive Definition: An ordered list of numbers generated by
continuously multiplying a value (the common ratio) with a given
first term.
a=3 3, 6, 12, 24, 48, ...
r=2
(ii) Implicit Definition: An ordered list of numbers where each
number in the list is generated by an exponential equation.
(n - 1)
t n = 3(2) 3, 6, 12, 24, 48, ...

Common Ratio (r):
(i) The number that is repeatedly multiplied to successive terms in
a geometic sequence.
a=3
r=2
(ii) From the implicit definition, r is the base of the exponential
function.
(n - 1)
t n = 3(2)

To Find The Common Ratio
r is the common ratio
tn is an arbitrary term in the sequence
t(n - 1) is the term immediately before tn in the sequence
3, 6, 12, 24, 48, ...

To Find the nth Term In a Geometic Sequence
tn is the nth term
a is the first term
n is the \"rank\" of the nth term in the sequence
r is the common ratio
3, 6, 12, 24, 48, ...

Once we know the pattern of a sequence, we can find any term of the
sequence. Use your calculator to check your answers.
Find the 110th term of: 5, 8, 11, 14, ... HOMEWORK
U(110)= 332
Find the 21st term of: 3, 6, 12, 24, ...
U(21)= 3 145 728

Find the 27th term of: 1, 1, 2, 3, 5, 8, ...
HOMEWORK
U(27)= 196 418

Which term in the sequence: 2, 5, 11, 23, 47, ... is 1535?
HOMEWORK

My cat is sick. His name is Little John and he has a cold. The vet has
given him some medicine. Each day he gets a pill with 35 mg of
medicine. His body eliminates 25% of the medicine each day and then
he gets another pill. HOMEWORK
(b) Will the amount of medicine in his body stabilize? How many days
will it take and how much medicine will be in his body?

My cat is sick. His name is Little John and he has a cold. The vet has
given him some medicine. Each day he gets a pill with 35 mg of
medicine. His body eliminates 25% of the medicine each day and then
he gets another pill. HOMEWORK
(a) How much medicine will be in his body in 5 days?
(b) Will the amount of medicine in his body stabilize? How many days
will it take and how much medicine will be in his body?

A small forest of 4000 trees is under a new forestry plan. Each year
20% of the trees will be harvested and 1000 new trees are planted.
(a) Will the forest ever disappear?
(b) Will the forest size ever stabilize? If so, how many years and
with how many trees?

A small forest of 4000 trees is under a new forestry plan. Each year
20% of the trees will be harvested and 1000 new trees are planted.
(a) Will the forest ever disappear?
(b) Will the forest size ever stabilize? If so, how many years and
with how many trees?

Introduction to today's class by Mr. Green on YouTube ...
a summary of almost everything in this unit ...
Sequences and Series on YouTube
http://youtube.com/watch?v=WjLSz-nNLBc

The Bouncing Ball
A ball is dropped from one metre, and the height is recorded
after each bounce. A 'Super Bouncer' sold locally is
guaranteed to bounce to 90 percent of its drop height if it is
dropped onto concrete from a height of less than two
metres.
1. How high does the ball bounce on its eighth bounce?
2. How many times does the ball bounce before it rises to
less than half of its original drop height?
3. How many times does the ball bounce before it stops bouncing?
4. How far has the ball travelled as it reaches the top of its 4th
bounce.
5. Construct a graph that shows the bounce height versus bounce
number.