Property of exponential functions

In summary, the statement "e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))" is not true and the advice given to solve the problem using properties of exponents is not applicable.
  • #1
Tricky557
7
0

Homework Statement



Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if:

e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))

Is a true statement or not. I've searched around the internet trying to find properties of adding/subtracting exponential functions, but I couldn't find anything.
 
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  • #2
You can turn the second term into [tex]e^{-\pi s}/e^{-2\pi s}[/tex]
from there multiply both sides by this denominator. This will reduce both the left and right side to one term. Do they equal?
 
  • #3
Tricky557 said:

Homework Statement


I'm stuck trying to figure out if:

e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))

Is a true statement or not.
This statement is not true. This only applies to multiplication of exponents.

axay=ax+y

Refer to this for exponential properties: http://www.efunda.com/math/exp_log/exp_relation.cfm

@Sandy: You are wrong as well. Your equation does not equal to the original problem
 
Last edited:
  • #4
Tricky557 said:

Homework Statement



Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if:

e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))

Is a true statement or not. I've searched around the internet trying to find properties of adding/subtracting exponential functions, but I couldn't find anything.
To answer your question, no, the left side is not equal to the right side.
 
  • #5
Ivan92 said:
@Sandy: You are wrong as well. Your equation does not equal to the original problem

He's not wrong, you just missed the part about him saying "the second term". But I find that advice to be quite useless if it still takes knowledge about exponential properties to determine the correct answer.
 

1. What is an exponential function?

An exponential function is a mathematical function in the form of f(x) = a^x, where a is a constant and x is the input variable. It is characterized by a rapid increase or decrease in value as x increases or decreases, respectively.

2. What is the property of growth in exponential functions?

The property of growth in exponential functions is that the function's output increases at a faster rate as the input increases. This is because the input is being multiplied by the constant a multiple times, resulting in an exponential growth.

3. How do you graph an exponential function?

To graph an exponential function, you can plot a few points by choosing values for x and then calculating the corresponding y values using the function. You can also use the properties of exponential functions, such as the y-intercept and the growth factor, to sketch the graph.

4. What is the difference between an exponential function and a linear function?

An exponential function has a variable in the exponent, while a linear function has a variable in the base. This results in a rapid increase or decrease in value for exponential functions, while linear functions have a constant rate of change.

5. What are some real-life applications of exponential functions?

Exponential functions are commonly used in finance, biology, and physics to model growth, decay, and other phenomena. For example, compound interest in finance can be modeled using an exponential function, while population growth in biology can be described by an exponential function. In physics, radioactive decay and the spread of diseases can also be modeled using exponential functions.

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