# Inverse Laplace for (e)^-5t*(t)^4

• bmed90
In summary, the student is working on finding the inverse Laplace for a function involving the exponential and polynomial terms. They attempted to use the Laplace table and properties, but encountered difficulties due to the multiplication of the two functions. After struggling for a few days, they found a better table and suggested deleting the post.
bmed90

## Homework Statement

Find:

Inverse Laplace for x(t)= (e)^-5t*(t)^4 using laplace table and laplace properties.

## The Attempt at a Solution

Well, I have been working on this problem for a few days now and cannot seem to figure it out. The two functions are not separate terms being added together so I cannot simply say

L^-1{(e)^-5t} + L^-1{(t)^4} which I originally tried. This would result in

1/s+5 + 24/s^5 which would be easy but since the two functions are being multiplied it is throwing me off and I cannot find an answer through the tables.

I found a better table, this post can be deleted

## 1. What is Inverse Laplace for (e)^-5t*(t)^4?

Inverse Laplace for (e)^-5t*(t)^4 refers to the process of finding the original function of a given Laplace transform that involves the variables e^-5t and t^4.

## 2. How is Inverse Laplace for (e)^-5t*(t)^4 calculated?

Inverse Laplace for (e)^-5t*(t)^4 can be calculated using the partial fraction method or by using a table of Laplace transforms to find the inverse transform of each term separately and then combining them.

## 3. What is the domain and range of the function (e)^-5t*(t)^4?

The domain of (e)^-5t*(t)^4 is all real numbers. The range is also all real numbers, as the exponential term ensures that the function will never reach zero.

## 4. How does the value of the constant 5 affect the graph of (e)^-5t*(t)^4?

The constant 5 affects the graph of (e)^-5t*(t)^4 by shifting the graph to the right by 5 units. This means that the function will start at t=5 instead of t=0.

## 5. Can the function (e)^-5t*(t)^4 have negative values?

Yes, the function (e)^-5t*(t)^4 can have negative values. This is because the exponential term e^-5t can have values between 0 and 1, while the polynomial t^4 can have both positive and negative values.

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