Real World EXAMPLES of Exponential and Logarithmic Functions

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Hey, is there anyone who can provide 2 graphical examples of either logarithmic or exponential functions relating to the real world. I've looked in many places and have given up. Please help.

Thanks in advance
 

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  • #4
symbolipoint
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Financial investments, bacterial growth rates and population sizes. These are not really specific examples - only general applications which you can also find in some textbooks. Slightly more specific application is savings bonds.
 
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epenguin
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The amount of a radioactive element remaining as a function of time. (negative exponential A(t) = A(0)*e^-kt). Similarly the amount of a chemical substance left as function of time when it reacts according to a 'first order' rate law -d[A]/dt = k[A] in many simple reactions. The amount of water left in a cylinder emptying as function of time if rate proportional to pressureThe charge left on a capacitor discharging without inductance as function of time. The density of gas under constant gravity as function of height . The rate of elementary chemical reaction as function of temperature. All negative exponentials some of them reflection fundamental physics (Maxwell distribution).
 
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yessir. I can.
My example is in the form of a word problem about Newton's Law of Cooling.
Its an example for modeling with Exponential and Logarithmic Equations:

Use Newton's Lay of Cooling, T = C + (T0 - C)e-kt, to solve this exercise. At 9:00 A.M., a coroner arrived at the home of a person who had died during the night. The temperature of the room was 70 degrees F, and at the time of death the person had a body temperature of 98.6 degrees F. The coroner took the body's temperature at 9:30 A.M., at which time it was 85.6 degrees F, and again at 10:00 A.M., when it was 82.7 degrees F. At what time did the person die??????

T = C + (T0 - C)e-kt
If you do not know what the variable's mean...these are their meanings:
T = temperature of a heated object
C = constant temperature of the surrounding medium (the ambient temp)
T0 = initial temperature of the heated object
k = negative constant associated with the cooling object
t = time (in minutes)
 

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