Properties 3 and 4 leads to a nice relationship between the logarithm and exponential function.
This lesson has several parts and each part has either individual work or partner work. We will go over each problem and discuss the problems as a class. The discussions will transition the class from activity to activity.
Consider the following steps with regard to vocabulary for struggling learners: Use of a graphic organizer e. Introduce new vocabulary using student friendly definitions and examples and non-examples. Review words with students.
Struggling learners may need to have these objectives written with examples provided. Use formative assessments throughout the lesson to determine level of student understanding.
Use follow-up reinforcement as necessary. Consider providing written examples for them. Consider providing a more student friendly definition with examples.
Struggling learners may not understand the formulas used or how you got them or when to know which form to use example: Instructional Procedures View This lesson can be fun for students because it illustrates how exponential and logarithmic functions are used in the real world.
Ask students whether they like crime shows or solving mysteries. Have a discussion about these shows or mysteries and what students like so much about them. Who can tell me what the most basic exponential equation is and what each part of the equation means? Most notably, exponential functions are used in population growth, interest, and bacterial growth.
Logarithmic functions are used to measure light and sound intensity, as well as measuring magnitudes of earthquakes. Review how to convert back and forth from exponential form to logarithmic form since students will be doing this when graphing logarithmic equations. We will begin with the equation, make a table of values with a few points, and sketch the graph.“Since a logarithmic function is the inverse of an exponential function, we simply graph the exponential function that is the inverse, draw the line of symmetry, y = x, and plot the reverse coordinates for each point on the exponential function.
An illustration will make this process easier to . This calculator will calculate the exponential function with the given base and exponent. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. Section Solving Exponential Equations. Now that we’ve seen the definitions of exponential and logarithm functions we need to start thinking about how to solve equations involving them.
Section Exponential Functions Exponential Function An exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f x() = a (1 + r)x or f x() = ab x where b = 1+ r Where.
Section Logarithms and Logarithmic Functions Rewriting Exponential Equations Work with a partner. Find the value of x in each exponential equation.
Explain your reasoning. Then use the value of x to rewrite the exponential equation in its equivalent logarithmic form, x = log b y.
a. A function is a relation in which each element of the domain is paired with exactly one element in the range. Two types of functions are the exponential functions and the logarithmic functions.