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I am both a Mechanical and an Electrical engineer ( aka use math in real life every day) and I work every day with systems described by exponential or logarithmic functions.
Just to name a few:
- Charging or discharging of a capacitor
- Any LRC circuit (or any combination thereof)
- Any SMD system (or any combination thereof)
- radioactive decay
- algorithmic efficiency
In other words, if you want to describe a real life you will probably encounter some exponential function. This comes from the fact that the solution to differential equations ( which govern most of the universe) generally contain an exponential term.
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How can you use logarithmic and exponential equations and properties to solve half-life and logistic growth scenarios?
For an exponential function: General equation of exponential decay is A(t)=A0e^-at The definition of a half-life is A(t)/A0=0.5, therefore: 0.5 = e^-at ln(0.5)=-at t= -ln(0.5)/a For exponential growth: A(t)=A0e^at Find out an expression to relate A(t) and A0 and you solve as above
Real life situation modeled by a function?
Suppose x people are eating at a (really cheap) buffet which costs $2 a person. Then the cost y is y = 2x. With a $3 off coupon it becomes y = 2x-3 (however I'm sure that most restaurants would want a sufficient number of people to make profit). Many other real-life applications are modeled using other functions. The bell curve is among the most common form, as it is used in statistics and distributions. Population models use a logistics function, another type of transcendental function. The catenary curve occurs when a chain or power line hangs on two ends, and is modeled by the hyperbolic cosine function y = cosh(x).
Example of a real life linear function?
Linear functions are used to model situations that show a constant rate of change between 2 variables. For example, the relation between feet and inches is always 12 inches/foot. so a linear function would be y = 12 x where y is the number of inches and x is the number of feet. y = 24 x models the number of hours in any given number of days {x}. Business applications abound. If a cell phone company charges a start-up fee of $50 and then $.05 for every minute used, the function is y = .05 x + 50.
What is impulsive system in differential equation?
A differential equation have a solution. It is continuous in the given region, but the solution of the impulsive differential equations have piecewise continuous. The impulsive differential system have first order discontinuity. This type of problems have more applications in day today life. Impulses are arise more natural in evolution system.
How can you relate operations on whole numbers in your daily life?
how do whole number relate to everday life
