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9-12 Algebra 2 Unit 5 Lesson 15

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 Geometry •Algebra 2 Extra Support Materials for Algebra 1

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Unit 1 Unit 2 Unit 3 Unit 4 •Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 •Lesson 15 Lesson 16 Lesson 17 Lesson 18

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Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

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Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

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Unit 5, Lesson 15

Using Graphs and Logarithms to Solve Problems (Part 1)

Algebra 2

Practice

Problem 1

Student Task Statement

The equation represents a bacteria population as a function of time in hours. Here is a graph of the function .

<p>Exponential growth function p of h = 5,000 times 2 to the power of h. Point on graph is about 4 point 4 comma 10,000. </p>

Use the graph to determine when the population will reach 100,000.
Explain why also tells us when the population will reach 100,000.

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Problem 2

Student Task Statement

Technology required. Population growth in the U.S. between 1800 and 1850, in millions, can be represented by the function , defined by , where represents the number of years after 1800.

What does estimate for the U.S. population in 1800?
Use graphing technology to graph the equations and . Adjust the graphing window to these boundaries: and .
What is the point of intersection of the two graphs, and what does it mean in this situation?

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Problem 3

Student Task Statement

The growth of a bacteria population is modeled by the equation , where is the number of hours after the population is first estimated. For each question, explain or show how you know.

How long does it take for the population to double?
How long does it take for the population to reach 1,000,000?

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Problem 4

ForLesson 10: Interpreting and Writing Logarithmic Equations

Student Task Statement

What value of makes each equation true?

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Problem 5

ForLesson 11: Evaluating Logarithmic Expressions

Student Task Statement

Put the following expressions in order, from least to greatest.

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Problem 6

ForLesson 14: Solving Exponential Equations

Student Task Statement

Solve . Show your reasoning.

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Problem 7

ForLesson 14: Solving Exponential Equations

Student Task Statement

Explain why is greater than 1 but is less than 2.

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Lesson 15 Resources

Student Materials