Sequences and Series as Models

Using them in real life (11.7)

POD Review

Suppose you have a flea circus, with a specially trained flea. Starting from the center of the ring, this flea jumps half of the distance remaining to the outside of the ring.

Will this flea ever reach the edge?

How could you show this with an equation?

POD Review

Suppose you have a flea circus, with a specially trained flea. Starting from the center of the ring, this flea jumps half of the distance remaining to the outside of the ring.

Will this flea ever reach the edge? Really, yes. Mathematically, no.

POD Review

Suppose you have a flea circus, with a specially trained flea. Starting from the center of the ring, this flea jumps half of the distance remaining to the outside of the ring.

How could you show this with an equation?

This is a geometric series. The first term is ½ and r = ½. Add the first 10 jumps.

POD Review

Suppose you have a flea circus, with a specially trained flea. Starting from the center of the ring, this flea jumps half of the distance remaining to the outside of the ring.

How could you show this with an equation?

This is a geometric series. The first term is ½ and r = ½. Add the first 10 jumps. After a number of jumps, he comes close, but the distance never actually reaches 1.

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Real world #1

You buy new blue jeans, and need them to fade. Every time you wash them, they lose 4% of the color they have just before they were washed.

Is this a geometric or arithmetic sequence? Why?

Real world #1

You buy new blue jeans, and need them to fade. Every time you wash them, they lose 4% of the color they have just before they were washed.

How much color is left after 10 washings?

Real world #1

You buy new blue jeans, and need them to fade. Every time you wash them, they lose 4% of the color they have just before they were washed.

How much color is left after 10 washings?

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Real world #1

You buy new blue jeans, and need them to fade. Every time you wash them, they lose 4% of the color they have just before they were washed.

If you want them to lose 75% of their original color, how many times should you wash them?

Real world #1

You buy new blue jeans, and need them to fade. Every time you wash them, they lose 4% of the color they have just before they were washed.

If you want them to lose 75% of their original color, how many times should you wash them?

So, after about 35 washes.

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Real world #2

Your little brother is hard up for cash and borrows 10 cents from you, at 5% interest, compounded daily.

Suppose you both forget the deal. How much does he owe you after a week?

Real world #2

Your little brother is hard up for cash and borrows 10 cents from you, at 5% interest, compounded daily.

You forget for a long time. How much does he owe you after a year?

Real world #2

Your little brother is hard up for cash and borrows 10 cents from you, at 5% interest, compounded daily.

At what point does he owe you a dollar?

Real world #3

You run a pile driving company, and mark the performance of your equipment. In the soil around Atlanta, your standard pile driver drives 100 cm. into the ground on the first impact, and 96 cm. on the second impact.

If this is the start of an arithmetic sequence, how far does the 10th impact move?

Real world #3

You run a pile driving company, and mark the performance of your equipment. In the soil around Atlanta, your standard pile driver drives 100 cm. into the ground on the first impact, and 96 cm. on the second impact.

How far in total has the driver moved after 10 impacts?

Real world #3

You run a pile driving company, and mark the performance of your equipment. In the soil around Atlanta, your standard pile driver drives 100 cm. into the ground on the first impact, and 96 cm. on the second impact.

At what point will it not move any more, and how far has it driven?