(1/z)(dz/dt) = 5
When z(1)=5
Ok so I get z=Ae^(5t) as an intermediate step, I think I got something wrong up until this point?
The books answer is z=5e^(5t-5)

Question

(1/z)(dz/dt) = 5
When z(1)=5 
Ok so I get z=Ae^(5t) as an intermediate step, I think I got something wrong up until this point?  
The books answer is z=5e^(5t-5)   <---- Fixed

anonymous · Answer

Wait! I fixed the problem

zepdrix · Answer

Oh good you fixed it hehe.

zepdrix · Answer

You are totally on the right track. Don't worry.
Your next step will be to use your `initial condition` that was given, to solve for A.

anonymous · Answer

Im unsure how the -5 gets in the 5t-5 on the exponent of e

zepdrix · Answer

Your A will involve an exponential of base e, they simplified the answer.
You'll see after you find your A.

anonymous · Answer

ok so I set z=5, so 5=Ae^((5(1))

anonymous · Answer

I totally can't solve for A, its embarrassing but....

zepdrix · Answer

hehe.
Divide both sides by e^5.

You'll end up with something like this,$$\large A=\frac{5}{e^5} \qquad \rightarrow \qquad A=5e^{-5}$$

anonymous · Answer

ok one second,,,

anonymous · Answer

SON of a!   argh I hate hate hate this sometimes. 
Thanks so much without you I would have just died.

anonymous · Answer

THe book combines the e ^  to one e 
I get it now

zepdrix · Answer

hah XD Yah it's a nice easy problem.
When the book over-simplifies things, they can be difficult to recognize.