1 Attachment(s)

Function constants and what they mean!

I am having problems interpreting a function. A container is supplied with water at a rate given by the equation in attachment 1 (photo1).

Which denotes a function of the time t, where V and k are positive constants. What does the constant V denote in this function?

Does V denote the initial volume of the water body at time t = 0?

Re: Function constants and what they mean!

$\displaystyle V(0) = \dfrac{1}{\sqrt{2}} V_0 e^{-k(0)}\sqrt{1+e^{-k(0)}} = \dfrac{1}{\sqrt{2}} V_0 \sqrt{1+1} = V_0$

So, yes, $\displaystyle V_0$ is the initial volume.

Re: Function constants and what they mean!

Thank you. I have been trying to integrate this expression, but unsure of what to do when given several constants. Any advice on how to approach this?