Answer to Question #337772 in Algebra for solomon

Question

Reflect on the concept of exponential and logarithm functions. What concepts (only the names) did you need to accommodate these new concepts in your mind? What are the simplest exponential and logarithmic functions with base b ≠ 1 you can imagine? In your day to day, is there any occurring fact that can be interpreted as exponential or logarithmic functions? What strategy are you using to get the graph of exponential or logarithmic functions?

Answer 1

Reflect on the concept of exponential and logarithm functions. Reflecting on the concept of exponential and logarithm functions, I can say that of course these functions are the opposite of each other. For instance, the logarithm function (y = logax) is the inverse equivalent of the exponential function (x = ay). With a parent exponent f(x) = ax always has a horizontal line at y=0, unless when a =1 and the slope of the function continuously increases as x increases. Graphically these equations are represented as big curves. This is why these functions are primarily used for rapid change or growth cases and study. Moreover it is always to remember that positive numbers cannot be raised to a negative number.

What concepts (only the names) did you need to accommodate these new concepts in your mind? exponent raised to the power logarithm Inverse Properties Natural logarithm functions Natural exponential functions Changing the base exponential growth compound interest common logarithm

What are the simplest exponential and logarithmic functions with base b ≠ 1 you can imagine? The simplest exponential and logarithmic functions with base b ≠ 1 are simply, y=bx and y= log bx respectively.

In your day to day, is there any occurring fact that can be interpreted as exponential or logarithmic functions? In our day to day, there are many occurring real-world situations that can be interpreted as exponential or logarithmic functions. For instance, The magnitude of an earthquake is a Logarithmic scale. The exponential or logarithmic are commonly

used as function models to compute bacterial culture, population growth, carbon date artifacts and many other cases where the numeric calculations is elaborate. In finance also they are massively used to calculate investment. In fact compounding creates exponential returns and savings accounts with a compounding interest rate can show exponential growth.

Also the measurement of the sound loudness in decibel formula is represented as a exponential function.

What strategy are you using to get the graph of exponential or logarithmic functions? Basically I use the graph calculator of Desmos that is the easiest and reliable tool at out service. Otherwise I could use a table with input and output where replacing the values in my equation I can have more points as possible to get my curve. It is a bit longer and graphically obviously less accurate but this is my method with not using technology.

Reflect on the concept of exponential and logarithm functions. Reflecting on the concept of exponential and logarithm functions, I can say that of course these functions are the opposite of each other. For instance, the logarithm function (y = logax) is the inverse equivalent of the exponential function (x = ay). With a parent exponent f(x) = ax always has a horizontal line at y=0, unless when a = and the slope of the function continuously increases as x increases. Graphically these equations are represented as big curves. This is why these functions are primarily used for rapid change or growth cases and study. Moreover it is always to remember that positive numbers cannot be raised to a negative number.

What concepts (only the names) did you need to accommodate these new concepts in your mind? Exponent Raised to the power Logarithm Inverse Properties Natural logarithm functions Natural exponential functions Changing the base Exponential growth Compound interest Common logarithm

What are the simplest exponential and logarithmic functions with base b ≠ 1 you can imagine? The simplest exponential and logarithmic functions with base b ≠ 1 are simply, y=bx and y= log bx respectively.