Unit 5 Exponential and Logarithmic Functions
Find exact and estimated values of logarithms.
Make conjectures about logarithm properties.
In this lesson, we found exact and approximate values for logarithmic expressions. We drew conclusions about properties of logarithms that are always true. We also identified characteristics of logarithmic functions that will help us to graph logarithms in the next lesson.
Identify and explain common features of the graphs of exponential functions.
Identify and explain common features of the graphs of logarithmic functions.
Transform the graph of an exponential or logarithmic function.
In this lesson, we graphed exponential and logarithmic functions by hand and used technology to determine common features in the graphs. We used technology to identify how the transformations appear in the equations of exponential functions. We examined graphs and wrote equations for the transformed functions, and we graphed transformed functions given the equations.
Model the growth of an invasive species.
Explain why exponential functions are good models for unchecked population growth.
Relate expressions with rational exponents to the growth of a population.
In this lesson, we learned how to change the form of exponential functions to reflect different rates of growth over different intervals of time. We used the rules of exponents to make equivalent functions. We interpreted exponential expressions in terms of a context by interpreting both the base of the expression and the exponent.
Use logarithms to solve exponential equations.
Solve systems of equations that contain exponential functions.
In this lesson, we found solutions to base
Model the growth of a savings account earning compound interest.
Solve exponential equations using logarithms.
In this lesson, we modeled the growth of a savings account earning compound interest with an exponential function. We interpreted the compound interest formula to understand how it changes when the number of compounding periods each year is changed. We learned to use logarithms to solve exponential equations of any base when the variable is in the exponent.