# using k as a constant

• April 24th 2008, 03:56 PM
sandiego234
using k as a constant
If dP/dt=.075P,
Find a formula for P in terms of t if P(0)=500.

Thanks
• April 24th 2008, 04:00 PM
TheEmptySet
Quote:

Originally Posted by sandiego234
If dP/dt=.075P,
Find a formula for P in terms of t if P(0)=500.

Thanks

$\frac{dP}{P}=.075dt$

integrate both sides to get

$ln|P|=.075t+c \iff P=e^{.075t+c}=e^{c}\cdot e^{.075t}$

$P=Ae^{.075t}$

Just plug in the intial condition and your done.