The Mathematics of Bouncing

(AKA Geometric Sequences)

boy bouncing a big blue ball by flickr user sean dreilinger

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

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.

(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) How much medicine will be in his body in 5 days?

Working with Sequences on the TI-83+ or 84+

A good resource for learning your way around the calculator or to review what we've learned in class ...

http://www.mathbits.com/MathBits/TISection/PreCalculus/sequences.htm

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.

(b) Will the forest size ever stabilize? If so, how many years and with how many trees?

(a) Will the forest ever disappear?

Sequences and Series on YouTube

Introduction to today's class by Mr. Green on YouTube ... a summary of almost everything in this unit ...

http://youtube.com/watch?v=WjLSz-nNLBc

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

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?

5. Construct a graph that shows the bounce height versus bounce number.

4. How far has the ball travelled as it reaches the top of its 10th bounce.

3. How many times does the ball bounce before it stops bouncing?

2. How many times does the ball bounce before it rises to less than half of its original drop height?

1. How high does the ball bounce on its eighth bounce?

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.

2. How many times does the ball bounce before it rises to less than half of its original drop height?

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.

3. How many times does the ball bounce before it stops bouncing?

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.

4. How far has the ball travelled as it reaches the top of its 10th bounce.

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. HOMEWORK

5. Construct a graph that shows the bounce height versus bounce number.

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. HOMEWORK