Real World EXAMPLES of Exponential and Logarithmic Functions

In summary, the conversation discusses the need for two graphical examples of either logarithmic or exponential functions in real-world applications. Examples given include exponential growth in biology/chemistry, financial investments, bacterial growth rates, population sizes, savings bonds, radioactive decay, chemical reactions, water emptying from a cylinder, capacitor discharge, gas density, and elementary chemical reactions. Additionally, an example word problem using Newton's Law of Cooling is provided to demonstrate the use of exponential and logarithmic equations in modeling real-world scenarios.
  • #1
sillydude
21
0
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
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.
 
  • #5
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).
 
Last edited:
  • #6
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)
 

1. What are some real world examples of exponential functions?

Exponential functions can be found in many natural phenomena, such as population growth, compound interest, and radioactive decay. For example, the growth of a bacteria population can be modeled by an exponential function.

2. How are logarithmic functions used in the real world?

Logarithmic functions are commonly used to represent data that grows exponentially, such as the Richter scale for measuring earthquake intensity or the pH scale for measuring acidity. They can also be used in finance to calculate the time needed to double an investment.

3. Can you provide an example of an exponential function in business?

One example is the growth of a company's profits over time. As the company expands and increases its revenue, its profits will also grow exponentially due to factors such as economies of scale.

4. How do exponential and logarithmic functions relate to each other?

Exponential and logarithmic functions are inverse operations of each other. This means that if an exponential function models the growth of a quantity, the corresponding logarithmic function can be used to find the time needed to reach a certain value.

5. What is a common misconception about exponential and logarithmic functions?

One common misconception is that exponential functions always represent rapid growth, while logarithmic functions always represent slow growth. In reality, the rate of growth can vary greatly depending on the specific parameters and context of the function.

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