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- https://math.libretexts.org/Courses/Quinebaug_Valley_Community_College/MAT186%3A_Pre-calculus_-_Walsh/04%3A_Exponential_and_Logarithmic_Functions/4.07%3A_Exponential_and_Logarithmic_ModelsWe have already explored some basic applications of exponential and logarithmic functions. In this section, we explore some important applications in more depth, including radioactive isotopes and New...We have already explored some basic applications of exponential and logarithmic functions. In this section, we explore some important applications in more depth, including radioactive isotopes and Newton’s Law of Cooling.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q2/02%3A_Applications_of_Integration/2.09%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_300%3A_Mathematical_Ideas_Textbook_(Muranaka)/06%3A_Miscellaneous_Extra_Topics/6.03%3A_Growth/6.3.02%3A_Special_Cases-_Doubling_Time_and_Half-LifeIf D is the doubling time of a quantity (the amount of time it takes the quantity to double) andP0 is the initial amount of the quantity then the amount of the quantity present after t ...If D is the doubling time of a quantity (the amount of time it takes the quantity to double) andP0 is the initial amount of the quantity then the amount of the quantity present after t units of time is P(t)=P0(2)tD If H is the half-life of a quantity (the amount of time it takes the quantity be cut in half) and P0 is the initial amount of the quantity then the amount of the quantity present after t units of time is
- https://math.libretexts.org/Courses/Mission_College/Math_001%3A_College_Algebra_(Kravets)/06%3A_Exponential_and_Logarithmic_Functions/6.07%3A_Exponential_and_Logarithmic_ModelsWe have already explored some basic applications of exponential and logarithmic functions. In this section, we explore some important applications in more depth, including radioactive isotopes and New...We have already explored some basic applications of exponential and logarithmic functions. In this section, we explore some important applications in more depth, including radioactive isotopes and Newton’s Law of Cooling.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_6%3A_Applications_of_Integration/6.8%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.08%3A_Exponential_Growth_and_Decay/2.8E%3A_Exercises_for_Section_2.8This page features true or false exercises focused on exponential functions, including growth and decay, along with financial calculations. It offers solutions and explanations for problems related to...This page features true or false exercises focused on exponential functions, including growth and decay, along with financial calculations. It offers solutions and explanations for problems related to population growth models, radioactive decay, interest rates, and more. Specific topics include calculating doubling times, analyzing population changes, and understanding temperature dynamics.
- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.05%3A_Exponential_and_Logarithmic_Functions/1.5.08%3A_Applications_of_Exponential_and_Logarithmic_FunctionsThe percentage of carbon-14 after some amount of time, t, (which we are trying to find) is 20%. Using decimals for the percent, we can substitute in M0=1 and M(t)=0.2 into the functi...The percentage of carbon-14 after some amount of time, t, (which we are trying to find) is 20%. Using decimals for the percent, we can substitute in M0=1 and M(t)=0.2 into the function we found in the previous example, \[\begin{align*}M(t)&=M_0e^{\left (-\tfrac{\ln(2)}{5730} \right )t}\\[4pt] 0.2&=1\cdot e^{\left (-\tfrac{\ln(2)}{5730} \right )t} \\[4pt] 0.2&=e^{\left (-\tfrac{\ln(2)}{5730} \right )t} \\[4pt] \ln0.2&=\frac{-\ln(2)}{5730}t\\[4pt] -\dfrac{5730}{\ln2}(\ln0.2)&=t\…
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/06%3A_Applications_of_Integration/6.08%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus_(2e)/04%3A_Exponential_and_Logarithmic_Functions/4.07%3A_Exponential_and_Logarithmic_ModelsThis section explores real-world applications of exponential and logarithmic functions, including population growth, radioactive decay, carbon-14 dating, logistic growth, and Newton’s Law of Cooling. ...This section explores real-world applications of exponential and logarithmic functions, including population growth, radioactive decay, carbon-14 dating, logistic growth, and Newton’s Law of Cooling. It explains key concepts such as doubling time and half-life, showing how these models are used in scientific and financial contexts. Examples illustrate how to apply these functions to solve practical problems.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2420_Calculus_II/02%3A_Applications_of_Integration/2.08%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
- https://math.libretexts.org/Courses/Mission_College/Mission_College_MAT_003B/04%3A_Introduction_to_Differential_Equations/4.03%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
