Exponential Growth and Decay Find the solution to dy/dt=4y satisfying y(4)=9. I am not sure where to begin. If I can get help with that I am sure I can finish the problem.

ubwicanyil5

ubwicanyil5

Answered question

2022-09-02

Exponential Growth and Decay
Find the solution to d y d t = 4 y satisfying y(4)=9. I am not sure where to begin. If I can get help with that I am sure I can finish the problem.

Answer & Explanation

Vaughn Greer

Vaughn Greer

Beginner2022-09-03Added 15 answers

1 y d y = 4 d t 1 y d y = 4 d t ln y = 4 t + C
Now use the fact that y=9 when t=4.
ln ( 9 ) = 4 ( 4 ) + C
So, C=ln9−16, which gives
y = e 4 t + ( ln 9 16 ) = e ln 9 e 4 t 16 = 9 e 4 t 16 .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?