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Lesson 3.14 Applications of geometric Sequences

Lesson 3.14 Applications of geometric Sequences. Concept: Geometric Sequences. EQ: How do we use geometric sequences to solve real world problems? F.LE.2. Vocabulary: Geometric sequence, common ratio, recursive formula, explicit formula, Null/ Zeroth Ter m. What do you remember relay.

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Lesson 3.14 Applications of geometric Sequences

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  1. Lesson 3.14Applications of geometric Sequences Concept: Geometric Sequences EQ: How do we use geometric sequences to solve real world problems? F.LE.2 Vocabulary: Geometric sequence, common ratio, recursive formula, explicit formula, Null/Zeroth Term

  2. What do you remember relay • Get into groups of 5 and line up one behind the other. • Each person will need a pen or pencil. • The person in front will also need a piece of paper. • Think back to the lesson over geometric sequences and when I say “GO” the person in front will write something they remember about geometric sequences and then pass it to the person behind them. The next person will add to it by either writing something new or adding to something that somebody already wrote. • Each person will have no more than 30 seconds. • When the last person finishes writing they will run the paper up to the first person in line and then sit. • 1 point will be awarded for every fact, 2 points for formulas, and 3 points for examples. • The team that finishes first will get 3 extra points. • The team that has the most points wins.

  3. How to identify a geometric sequence • In a word problem, look for a common ratio being used between each term. • Example: • Determine whether each situation has a common ratio between each term. • The bacteria tripled each day. • Malik earns $15 an hour at his job. • The value of a new car decreases by 9% each year.

  4. Steps to finding a term for a geometric sequence • Create a pictureof the word problem. • Write out the sequence in order to identify the common ratio, and the first term, • Determine which formula would best fit the situation (Recursive or Explicit) • Substitute and in to the formula from step 3. • Evaluate the formula for the given term. • Interpret the result.

  5. Example 1 • On a Saturday, you sit in your yard and decide to count the number of dandelions that you see. You count a total of 39 dandelions. On Sunday, you count 78 dandelions and on Monday you count 156. If this pattern continues, how many dandelions will there be in your yard on Friday?

  6. Example 1: Sequence Picture Formula Interpretation

  7. Example 2 • Suppose you drop a ping pong ball from a height of 20 feet. After the ball hits the ground, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round your answer to the nearest tenth.

  8. Example 2: Sequence Picture Formula Interpretation

  9. Example 3 • You and your family go on vacation and stay at a hotel. You go down to the pool area to soak in the hot tub. To your disappointment, the water is freezing cold. You complain to the manager and she tells you that she will increase the temperature by 10% each hour. If the current temperature of the hot tub is 65° F, what will be the temperature of the hot tub after 4 hours, to the nearest tenth of a degree?

  10. Example 3: Sequence Picture Formula Interpretation

  11. You Try! • You open a savings account with $350 that you have saved. The bank offers 2.8% simple interest each year. How much money will you have in your account after 10 years?

  12. You Try! Sequence Picture Formula Interpretation

  13. 3-2-1 Summarizer • Name 3 facts you already knew prior to the lesson today. • Name 2 new facts you learned today. • Name 1 skill that you still need practice.

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