Is this also correct, if it is wrong please help
2 answers:
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Answer:
k = 30,
Step-by-step explanation:
Since is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that
Then, replacing the derivatives in the equation we have:
Since is a positive function, we have that
.
Now, consider a general solution , then, by calculating the derivatives and replacing them in the equation, we get
We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.
Therefore, the general solution is
We are asked to express r in terms of A, P, and t.
We first divide both sides of the equation by t, which gives us
,
then, dividing both sides by P, we have
.
Swap the sides:
Finally subtracting 1 from both sides gives us
.
We first divide both sides of the equation by t, which gives us
then, dividing both sides by P, we have
Swap the sides:
Finally subtracting 1 from both sides gives us