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9-12 Integrated Math 3 Unit 4 Lesson 20

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K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

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

Modeling Prompts

Lesson

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 Lesson 19 •Lesson 20 Lesson 21 Lesson 22 Lesson 23

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6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
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Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Modeling Prompts

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Lesson 11
Lesson 12
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Lesson 20
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Lesson 23

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Unit 4, Lesson 20

Using Graphs and Logarithms to Solve Problems (Part 1)

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Integrated Math 3

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 .

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 20 Resources

Student Materials