At the beginning of his diet, jack weighed 240 4/5 pounds. At the end of the diet, he weighed 3/4 his original weight. What did
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Answer:
Step-by-step explanation:
The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:
A differential equation of the form:
Will have a characteristic equation of the form:
Where solutions are the roots from which the general solution can be found.
For real roots the solution is given by:
For real repeated roots the solution is given by:
For complex roots the solution is given by:
Where:
Let's find the solution for using the previous information:
The characteristic equation is:
So, the roots are given by:
Therefore, the solution is:
As you can see, is the same solution provided by the problem.
Moving on, let's find the derivative of in order to find the constants
and
:
Evaluating the initial conditions:
And
Now we have found the value of the constants, the solution of the second-order IVP is:
Here we use the equation
Taking points (0,4), (1,2)
Substituting the point (0,4) , we will get
Substituting (1,2) we will get
So we have
Therefore , required equation is