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- https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/01%3A_Functions_and_Graphs/1.05%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/01%3A_Review-_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsWe use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number \(e\).We also define hyperbolic and invers...We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number \(e\).We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. (Note that we present alternative definitions of exponential and logarithmic functions in the chapter Applications of Integrations, and prove that the functions have the same properties with either definiti…
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/1%3A_Functions_and_Graphs_(Review)/1.5%3A_Exponential_and_Logarithmic_FunctionsWe use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number \(e\).We also define hyperbolic and invers...We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number \(e\).We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. (Note that we present alternative definitions of exponential and logarithmic functions in the chapter Applications of Integrations, and prove that the functions have the same properties with either definiti…
- https://math.libretexts.org/Under_Construction/Purgatory/MAT_1320_Finite_Mathematics/07%3A_Exponential_and_Logarithmic_Functions/7.01%3A_Exponential_Growth_and_Decay_ModelsIf \(x\) = the number of months that have passed and \(y\) is the number of users, the number of users after \(x\) months is \(y = 10000+1500x\). For each site, use the function to calculate the numbe...If \(x\) = the number of months that have passed and \(y\) is the number of users, the number of users after \(x\) months is \(y = 10000+1500x\). For each site, use the function to calculate the number of users at the end of the first year, to verify the values in the table. A population of bacteria is given by the function \(y = f(t) = 100(2)^t\), where \(t\) is time measured in hours and \(y\) is the number of bacteria in the population.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q1/01%3A_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_1320_Finite_Mathematics_2e/05%3A_Exponential_and_Logarithmic_Functions/5.01%3A_Exponential_Growth_and_Decay_ModelsIf \(x\) = the number of months that have passed and \(y\) is the number of users, the number of users after \(x\) months is \(y = 10000+1500x\). For each site, use the function to calculate the numbe...If \(x\) = the number of months that have passed and \(y\) is the number of users, the number of users after \(x\) months is \(y = 10000+1500x\). For each site, use the function to calculate the number of users at the end of the first year, to verify the values in the table. A population of bacteria is given by the function \(y = f(t) = 100(2)^t\), where \(t\) is time measured in hours and \(y\) is the number of bacteria in the population.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_1_(Beck)/01%3A_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
- https://math.libretexts.org/Courses/City_University_of_New_York/Calculus_I_(CUNY)/01%3A_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
- https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/01%3A_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
- https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/01%3A_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/01%3A_Functions_and_Graphs/1.06%3A_Exponential_and_Logarithmic_FunctionsThe exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of...The exponential function \(y=b^x\) is increasing if \(b>1\) and decreasing if \(0<b<1\). Its domain is \((−∞,∞)\) and its range is \((0,∞)\). The logarithmic function \(y=\log_b(x)\) is the inverse of \(y=b^x\). Its domain is \((0,∞)\) and its range is \((−∞,∞)\). The natural exponential function is \(y=e^x\) and the natural logarithmic function is \(y=\ln x=\log_e x\). Given an exponential function or logarithmic function in base \(a\), we can make a change of base to convert this function to a
