# Exponential Growth & Decay

• November 11th 2007, 05:47 PM
blurain
Exponential Growth & Decay
I'm not sure how to go about solving this problem, so any help will be much appreciated!

v'= 3 times the radical of t
v(1)= 3
v(4)= ?
• November 11th 2007, 08:33 PM
topsquark
Quote:

Originally Posted by blurain
I'm not sure how to go about solving this problem, so any help will be much appreciated!

v'= 3 times the radical of t
v(1)= 3
v(4)= ?

$v^{\prime} = 3\sqrt{t}$

So
$\int v^{\prime}~dt = \int 3 \sqrt{t}~dt$

$v(t) = 3 \cdot \frac{1}{\frac{3}{2}}t^{3/2} + C = 2\sqrt{t^3} + C$

Now use v(1) = 3 to find the value for C.

-Dan