Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/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/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/Mission_College/Math_3B%3A_Calculus_II_(Reed)/06%3A_Introduction_to_Differential_Equations/6.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/Mission_College/MAT_3B_Calculus_II_(Kravets)/06%3A_Introduction_to_Differential_Equations/6.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/07%3A_Introduction_to_Differential_Equations/7.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- 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/Community_College_of_Denver/MAT_2562_Differential_Equations_with_Linear_Algebra/04%3A_Applications_of_First_Order_Equations/4.02%3A_Cooling_and_MixingThis section deals with applications of Newton's law of cooling and with mixing problems.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_420%3A_Differential_Equations_(Breitenbach)/04%3A_Applications_of_First_Order_Equations/4.02%3A_Cooling_and_MixingBut Q′ is the rate of change of the quantity of salt in the tank changes with respect to time; thus, if rate in denotes the rate at which salt enters the tank and rate out denotes the rate by whic...But Q′ is the rate of change of the quantity of salt in the tank changes with respect to time; thus, if rate in denotes the rate at which salt enters the tank and rate out denotes the rate by which it leaves, then To determine the rate out, we observe that since the mixture is being removed from the tank at the constant rate of 2 liters/min and there are 2t+200 liters in the tank at time t, the fraction of the mixture being removed per minute at time t is
- 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\…
