Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 15
Math
Unit 5
11th Grade
Lesson 15 of 16
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Lesson Notes
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Use logarithms to solve exponential modeling problems (Part I).
The core standards covered in this lesson
A.SSE.A.1.B — Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)<sup>n</sup> as the product of P and a factor not depending on P.
F.LE.A.4 — For exponential models, express as a logarithm the solution to ab<sup>ct</sup> = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
The foundational standards covered in this lesson
F.LE.A.1.A — Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F.LE.A.1.B — Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LE.A.1.C — Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
A population of a city grows at 5% per year. The population in 1990 was 400,000. In what year do you predict the population will reach one million?
A bacteria doubles in size every six hours. Four hours from now, the culture has 8,000 bacteria. How many bacteria were there to start?
Algal blooms routinely threaten the health of the Chesapeake Bay. Phosphate compounds supply a rich source of nutrients for the algae, Prorocentrum minimum, responsible for particularly harmful spring blooms known as mahogany tides. These compounds are found in fertilizers used by farmers and find their way into the Bay with run-offs resulting from rainstorms. Favorable conditions result in rapid algae growth ranging anywhere from 0.144 to 2.885 cell divisions per day. Algae concentrations are measured and reported in terms of cells per milliliter (cells/ml). Concentrations in excess of 3,000 cells/ml constitute a bloom.
Algae Blooms, accessed on Feb. 23, 2018, 11:39 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
You deposit $8,000 into an account that pays 4.5% interest, compounded quarterly. How long will it take for you to have $12,000?
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Use logarithms to solve exponential modeling problems (Part II).
Topic A: Modeling with and Interpreting Exponential Functions
Identify, model, and analyze geometric sequences.
Standards
F.IF.A.3F.IF.B.5F.LE.A.2
Analyze and construct exponential functions that model contexts.
F.IF.B.4F.IF.C.8.BF.LE.A.2
Write and change the form of exponential functions that model compounding interest.
F.BF.A.1.AF.LE.B.5
Define and use $$e$$ in continuous compounding situations.
A.SSE.B.3.CF.BF.A.1.A
Describe the derivation of the formula for the sum of a finite geometric series and use it to solve problems.
A.SSE.B.4
Find the sum of an infinite geometric series.
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Topic B: Definition and Meaning of Logarithms
Describe and evaluate simple numeric logarithms (Part I).
F.LE.A.4
Describe and evaluate simple numeric logarithms (Part II).
Describe logarithms as the inverse of exponential functions and graph logarithmic functions.
F.BF.B.3F.BF.B.4.BF.BF.B.4.CF.BF.B.5F.IF.C.7.E
Evaluate common and natural logs using tables, graphs, and calculators.
F.BF.B.4.CF.LE.A.4
Understand and apply the change of base property to evaluate logarithms.
Develop and use the product and quotient properties of logarithms to write equivalent expressions.
Develop and use the power property of logarithms to write equivalent expressions.
F.BF.B.4.BF.LE.A.4
Solve equations with logarithms.
A.SSE.A.1.BF.LE.A.4
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