# Thread: rate of change help

1. ## rate of change help

water flows into a dam at a rate given by dv/dt = 30000 root (t+1)

Find the expression for the volume of water in the dam after t days assuming that the dam initially held 60000 m^3 of water

i tried integration of this equation
30000 root(t+1) + 60000

but i couldnt get the right answer which was 2000[2 + (t+1)^1.5]
any help greatly appreciated !

2. Originally Posted by flyinhigh123
water flows into a dam at a rate given by dv/dt = 30000 root (t+1)

Find the expression for the volume of water in the dam after t days assuming that the dam initially held 60000 m^3 of water

i tried integration of this equation
30000 root(t+1) + 60000

but i couldnt get the right answer which was 2000[2 + (t+1)^1.5]
any help greatly appreciated !

HI

I think the answer should be $\displaystyle V=20000[2+(t+1)^{\frac{3}{2}}]$

you integrated wrongly

$\displaystyle \frac{dv}{dt}=30000(t+1)^{\frac{1}{2}}$

$\displaystyle V=30000\int (t+1)^{\frac{1}{2}}$

= $\displaystyle 20000(t+1)^{\frac{3}{2}}+c$

When t=0 , V=60000

put that in , and you will find that c is 40000

Then simplify ..

3. thankyouu !!