# integral calculas???

• Nov 1st 2007, 02:06 AM
softdrink_jr
integral calculas???
r(t)=dr/dt=0.05e^.02t (200-t)

r(0)=1000

using integral calculas i need to show that r(t)=2.5e^.02t (250-t)+375

How is this found???
• Nov 1st 2007, 02:17 AM
Krizalid

But I could see that you need to solve a differential equation with initial condition.
• Nov 1st 2007, 02:42 AM
softdrink_jr
is this a little easier to understand???
If the rate of growth of the number of wasps at time t days is given by -

r(t)=dr/dt=0.05e^.02t (200-t), r(0)=1000

show that the number of reproductive wasp r(t) at time t equals -

2.5e^.02t (250-t)+375

• Nov 1st 2007, 04:10 AM
kalagota
Quote:

Originally Posted by softdrink_jr
If the rate of growth of the number of wasps at time t days is given by -

r(t)=dr/dt=0.05e^.02t (200-t), r(0)=1000

show that the number of reproductive wasp r(t) at time t equals -

2.5e^.02t (250-t)+375

is this what you want?

$r(t) = \frac{dr}{dt} = 0.05e^{0.02t}(200 - t)$
where $\, r(0)=1000$

and show that
$r(t) = 2.5e^{.02t} (250-t)+375$

but why is that $\, r(t) = \frac{dr}{dt}$?