Week 5 Learning Journal AG PDF

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Q.Reflect on the concept of exponential and logarithm functions. The exponential function is one of the mathematical functions which is useful and supports in finding the growth or decay of the population, money, price, etc that are increasing or decreasing exponentially. An exponential has a constant as its base and a variable as its exponent. If a function has a variable as the base and a constant as the exponent, it is a power function, not an exponent function. The inverses of exponential functions are known as the logarithm functions. Any kinds of the exponential function can be stated in logarithmic form. Then, all logarithmic functions can also be rewritten in exponential form. The the logarithm functions are useful in permitting us to work with enormous numbers while manipulating numbers of a much more manageable size (Cliffs Notes, n.d.). Q.What concepts (only the names) did you need to accommodate these new concepts in your mind? Exponent Logarithm Inverse function Powerful function Common logarithm Natural logarithm Compound interest Raised to the power Changing the base Exponential growth Rate of growth Increasing Decreasing Q.What are the simplest exponential and logarithmic functions with base b ≠ 1 you can imagine? The simplest exponential function with base b ≠ 1 is y = bx. The simplest logarithmic functions with base b ≠ 1 is y = log bx.

Q.In your day-to-day, is there any occurring fact that can be interpreted as exponential or logarithmic functions? Both exponential and logarithmic functions are used in our daily life. For exponential function, we use in microorganisms in culture to detect the disease, spoilage of food calculating with the temperature, human population, compound interest, cancer cell growth, burning fire to calculate the duration of burning, invasive species to calculate the damage to the environment, human economy and health, and the sale rate. For logarithmic functions, we use to measure sound intensity, pH value, bacteria growth, compound interest, the magnitude of earthquake, and so many. Q.What strategy are you using to get the graph of exponential or logarithmic functions? I use a table to get the graph of exponential or logarithm functions. First of all, I make a chart with x and y to represent my columns. Then, I put given equation from the question to Desmos Calculator and follow my inputs/outputs from my equation. To get a graph of an exponential function, I find the lower and upper limit of the function, the nature of the slope and proceed in studying the nature of the change of slope. To obtain a graph of a logarithmic function, I look at the condition of the base, the point at which it intersects the x-axis, its slope, and its nature. I mostly use is the Desmos Caculator. Then, I use Symbolab Calculator that mostly show me step by step how to solve the equation.

Word Count - 478 References Abramson, J., Falduto, V., Gross, R., Lippman, D., Rasmussen, M., Norwood, R., Belloit, N., Magnier, J.-M., Whipple, H., & Fernandez, C. (2015). Algebra and Trigonometry by OpenStax (Official Print Version, hardcover, full color) [E-book]. Open Stax. Cliffs Notes. (n.d.). Logarithmic Functions. https://www.cliffsnotes.com/study-guides/algebra/algebra-ii/exponential-and-logarithmic-functions/logarith mic-functions Desmos | Graphing Calculator. (n.d.). Desmos. https://www.desmos.com/calculator Quantitative Reasoning. (n.d.). Half-Life & Doubling-Time. http://matcmath.org/textbooks/quantitativereasoning/half-life-doubling-time/

Studious Guy. (2019, July 8). 10 Real Life Examples Of Exponential Growth. https://studiousguy.com/real-life-examples-exponential-growth/ Symbolab Math Solver. (n.d.). Symbolab. https://www.symbolab.com/...