Scribd
Upload
549 views2 pages

Exponential Equations LP

The document provides information about solving exponential equations. It begins with an introduction about half-life and using exponential functions to model radioactive decay. It then lists the learning objectives as being able to solve exponential equations. Various definitions and properties of exponents are reviewed. Exponential functions, equations, and inequalities are defined. Examples of each are provided. Steps for solving exponential equations are outlined as writing both sides with the same base and applying the one-to-one property of exponential functions. Sample problems demonstrate solving exponential equations using these steps. An assessment on the material concludes the document.

Uploaded by

Brian Mary
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
549 views2 pages

Exponential Equations LP

The document provides information about solving exponential equations. It begins with an introduction about half-life and using exponential functions to model radioactive decay. It then lists the learning objectives as being able to solve exponential equations. Various definitions and properties of exponents are reviewed. Exponential functions, equations, and inequalities are defined. Examples of each are provided. Steps for solving exponential equations are outlined as writing both sides with the same base and applying the one-to-one property of exponential functions. Sample problems demonstrate solving exponential equations using these steps. An assessment on the material concludes the document.

Uploaded by

Brian Mary
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 2

Department of Education

Region III
Division of Zambales
LIPAY NATIONAL HIGH SHOOL
School ID: 301034
Magsaysay Park, Poblacion South, Sta. Cruz, Zambales

Solving Exponential Equations


I. Introduction
Hugot ba Class? Eto ang matinding hugot, year 2002.

(Play the song, HALF-LIFE by Duncan Sheik)


“Maybe, I need to see the daylight
To leave behind the half-life
Don't you see I'm breaking down?”
– Duncan Shiek, Daylight (2002)

Exponential functions are used to model real-life situations such as population growth, carbon
dating, growth of an epidemic, loan interest rates, investments and of course, radioactive decay or half –
life.
The half-life of a radioactive substance is the time it takes for half of the substance to decay.

From the definition of half – life given, explain the meaning of the song.

Consider this problem: The half – life of Zn – 71 is 2.54 minutes. Initially, there were 𝑦0 grams of Zn –
1
71, but only 256 of this amount remains some time. How much time has passed?

II. Learning Competencies


At the end of the lesson, the learner is able to solve exponential equations (M11GM – Ie – f – 1)

III. Review
Have a recall the following definitions and theorems. (The LAWS of EXPONENT)
Definition. Let 𝑎 ≠ 0. We define the following:
1. 𝑎0 = 1
1
2. 𝑎−𝑛 = 𝑎𝑛

Theorems. Let 𝑟 and 𝑠 be rational numbers. Then,

1. 𝑎𝑟 𝑎 𝑠 = 𝑎𝑟+𝑠
𝑎𝑟
2. 𝑎𝑠
= 𝑎𝑟−𝑠
3. (𝑎𝑟 )𝑠 = 𝑎𝑟𝑠
4. (𝑎𝑏)𝑟 = 𝑎𝑟 𝑏 𝑟
𝑎 𝑟 𝑎𝑟
5. (𝑏 ) = 𝑏𝑟

IV. Presentation
The exponential function is one of the most important functions in mathematics (though it would
have to admit that the linear function ranks even higher in importance).
To form an exponential function, we let the independent variable be the exponent. A simple example is
the function 𝑓(𝑥) = 2𝑥 .
Exponential Equation
An equation involving exponential expressions.
1
Example. 72𝑥 =
343

Exponential Inequality
An inequality involving exponential expressions.
Example. 52𝑥 − 5𝑥+1 ≤ 0

Exponential Functions
Function of the form 𝑓(𝑥) = 𝑏 𝑥 (𝑏 > 0, 𝑏 ≠ 1).
Example. 𝑓(𝑥) = 1.8𝑥
Or 𝑦 = 5𝑥

V. Activity I
Determine whether the given is an exponential function, exponential equation, or exponential
inequality.
1. 𝑓(𝑥) = 5𝑥 2
1 𝑥
2. 2 ≥ (2)
3. 74𝑥 = 𝑦
4. 4(10𝑥−2 ) = 500
5. 7 < 14𝑥+3

VI. Activity II

To solve exponential equation, we must follow the steps:


Steps:
1. Write both sides with the same base.
2. Apply the one-to-one property.
3. Solve for the value of x.
One – to One Property of Exponential Functions
If 𝑥1 ≠ 𝑥2 , then 𝑏 𝑥1 ≠ 𝑏 𝑥2 . Conversely, if 𝑏 𝑥1 = 𝑏 𝑥2 , then 𝑥1 = 𝑥2

Example 1. Solve the equation 4𝑥−1 = 16. Example 2. Solve the equation 125𝑥−1 = 25𝑥+3 .
Solution. Write both sides with 4 as the base. Solution. Both 125 and 25 can be written using 5
4𝑥−1 = 16 as the base.
4𝑥−1 = 42 125𝑥−1 = 25𝑥+3
𝑥 −1 = 2 (53 )𝑥−1 = (52 )𝑥+3
𝑥 = 2 + 1 53(𝑥−1) = 52(𝑥+3)
𝑥 = 3 3(𝑥 − 1) = 2(𝑥 + 3)
3𝑥 − 3 = 2𝑥 + 6
𝑥=9

Solve for 𝑥 in the following exponential equations.


1. 3𝑥 = 81
2. 57−𝑥 = 125

VII. Assessment

The students will perform an assessment (10 items questions) based on the lesson using Interactive
PowerPoint. The question on the Introduction about Half-life can be answered on this section as Enrichment.

VIII. Generalization

Summary of the Lesson

Prepared by:

BRIAN M. MARY
Lipay National High School

You might also like