Notes 2 - Ms. Mader's Class Collective



Notes for 2.1

Killer Plant Strikes Lake Victoria

Pg. 20 – 21

Exponential growth occurs in many real life situations. For example, consider this story from 1998:

Plants like the water hyacinth that grow and spread rapidly can affect native plants and fish. This in turn can affect the livelihood of fishers. To understand how such plants grow, you will look at a similar situation.

Ghost Lake is a popular site for fishers, campers, and boaters. In recent years, a certain water plant has been growing on the lake at an alarming rate. The surface area of Ghost Lake is 25,000,000 square feet. At present 1,000 square feet are covered by the plant. The Department of Natural Resources estimates that the area is doubling every month.

1. What are the variables that will affect the growth of this plant?

________________________________________________________________________

2. Write an equation that represents the growth pattern of the plant on Ghost Lake. ______________________

3. Fill in the table to show the first 6 months of this plant’s affect.

|Month |Area Covered |

|1 | |

|2 | |

|3 | |

|4 | |

|5 | |

|6 | |

4. Make a graph of the above table. (Remember to LABEL)

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[pic]

5. How much of the lake will be covered by the end of the year? ______________sq. ft.

*Remember to convert 1 year into months for your equation to work.*

Homework:

1. If you don’t brush your teeth regularly, it won’t take long for large colonies of bacteria to grow in your mouth. Suppose a single bacterium lands on your tooth and starts to multiply by a factor of 4 every hour.

A. Write an equation that describes the number of bacteria b in the new colony after n hours. _______________________

B. How many bacteria will be in the colony after 7 hours? ____________

C. After 8 hours? ___________ How can you use the answer from question B to answer this? ______________________________________________________

D. After about how many hours will there be at least 1,000,000 bacteria in the colony?_________________

E. Suppose that instead of only 1 bacteria landing on your tooth, there were 50. Now write the equation again using this information. ___________________

2. Loon Lake has a killer plant problem similar to Ghost Lake. Currently 5,000 square feet of the lake is covered with the plant. The area covered is growing by a factor of 1.5 each year.

A. Complete the table below showing the growth rate of the killer plant.

|Year |Area Covered (sq. ft.) |

|0 | |

|1 | |

|2 | |

|3 | |

|4 | |

|5 | |

B. The surface are of the lake is 200,000 square feet. How long will it take before the entire lake is covered? ___________

C. Make a graph of the table. REMEMBER TO LABEL

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Notes for 2.1

Killer Plant Strikes Lake Victoria

Pg. 20 – 21

Exponential growth occurs in many real life situations. For example, consider this story from 1998:

Plants like the water hyacinth that grow and spread rapidly can affect native plants and fish. This in turn can affect the livelihood of fishers. To understand how such plants grow, you will look at a similar situation.

Ghost Lake is a popular site for fishers, campers, and boaters. In recent years, a certain water plant has been growing on the lake at an alarming rate. The surface area of Ghost Lake is 25,000,000 square feet. At present 1,000 square feet are covered by the plant. The Department of Natural Resources estimates that the area is doubling every month.

1. What are the variables that will affect the growth of this plant?

Answers can vary: rain fall, disturbance to the environment

2. Write an equation that represents the growth pattern of the plant on Ghost Lake.

A = 1000(2n)

3. Fill in the table to show the first 6 months of this plant’s affect.

|Month |Area Covered |

|1 |2000 |

|2 |4000 |

|3 |8000 |

|4 |16000 |

|5 |32000 |

|6 |64000 |

4. Make a graph of the above table. (Remember to LABEL)

Growth of the Lake Plant

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Area Covered

(sq. ft.)

0 1 2 3 4 5 6

Number of Months

[pic]

5. How much of the lake will be covered by the end of the year? 4,096,000 sq. ft.

*Remember to convert 1 year into months for your equation to work.*

Homework:

1. If you don’t brush your teeth regularly, it won’t take long for large colonies of bacteria to grow in your mouth. Suppose a single bacterium lands on your tooth and starts to multiply by a factor of 4 every hour.

A. Write an equation that describes the number of bacteria b in the new colony after n hours. B = 4n

B. How many bacteria will be in the colony after 7 hours? B = 16,384

C. After 8 hours? 65,536 How can you use the answer from question B to answer this?

You can use the answer from 47 and multiply it by 4.

D. After about how many hours will there be at least 1,000,000 bacteria in the colony?10 hours, B = 410 = 1,048,576 bacteria

E. Suppose that instead of only 1 bacteria landing on your tooth, there were 50. Now write the equation again using this information. B = 50(4n)

2. Loon Lake has a killer plant problem similar to Ghost Lake. Currently 5,000 square feet of the lake is covered with the plant. The area covered is growing by a factor of 1.5 each year.

A. Complete the table below showing the growth rate of the killer plant.

|Year |Area Covered (sq. ft.) |

|0 |5000 |

|1 |7500 |

|2 |11,250 |

|3 |16,875 |

|4 |25,312.5 |

|5 |37,968.75 |

B. The surface are of the lake is 200,000 square feet. How long will it take before the entire lake is covered? 10 years

C. Make a graph of the table. REMEMBER TO LABEL

Growth on Loon Lake

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Area Covered

0 1 2 3 4 5

Year

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TIP: To pick the values for the Area Covered, figure out what your top number must be and then compare that to the number of lines you have to work with. How much will each line need to be worth?

TIP: To pick the values for the Area Covered, figure out what your top number must be and then compare that to the number of lines you have to work with. How much will each line need to be worth?

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